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^r Texas 
Instruments 



Topics in 
Algebra 1 




^ Texas 
Instruments 



Topics in Algebra 1 



Software Application 

for the 

TI-83 Plus and the TI-73 



Student and Teacher 

Classroom Materials 

Chapters 1-5 



Important notice regarding book materials 

Texas Instruments makes no warranty, either expressed or implied, including 
but not limited to any implied warranties of merchantability and fitness for a 
particular purpose, regarding any programs or book materials and makes such 
materials available solely on an "as-is" basis. In no event shall Texas 
Instruments be liable to anyone for special, collateral, incidental, or 
consequential damages in connection with or arising out of the purchase or 
use of these materials, and the sole and exclusive liability of Texas 
Instruments, regardless of the form of action, shall not exceed the purchase 
price of this book. Moreover, Texas Instruments shall not be liable for any 
claim of any kind whatsoever against the use of these materials by any other 
party. 

Permission is hereby granted to teachers to reprint or photocopy in 
classroom, workshop, or seminar quantities the pages or sheets in this work 
that carry a Texas Instruments copyright notice. These pages are designed to 
be reproduced by teachers for use in their classes, workshops, or seminars, 
provided each copy made shows the copyright notice. Such copies may not be 
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Incorporated to reproduce or transmit this work or portions thereof in any 
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information storage or retrieval system, unless expressly permitted by federal 
copyright law. Send inquiries to this address: 



Texas Instruments Incorporated 
7800 Banner Drive, M/S 3918 
Dallas, TX 75251 

Attention: Manager, Business Services 



Copyright © 2001, 2002 Texas Instruments Incorporated. Except for the 
specific rights granted herein, all rights are reserved. 

Printed in the United States of America. 



H) Tip and (§ Try-It! are trademarks of Texas Instruments Incorporated. 



Table of Contents 
Introduction to Topics in Algebra 1 

Note to Teachers 

Organization of Topics in Algebra 1 

Classroom Materials 

NCTM Principles and Standards for School Mathematics 

Acknowledgements 

Installing This Application 

Deleting an Application 

Navigating Topics in Algebra 1 

Chapter 1 : Number Sense 
Section 1 : Integers 

Student Worksheet 
Teacher Notes 

Section 2: Rational Numbers 

Student Worksheet 
Teacher Notes 

Section 3: Real Numbers 

Student Worksheet 
Teacher Notes 

Chapter 2: Linear Equations 
Section 1 : Using Graphs & Tables 

Student Worksheet 
Teacher Notes 

Section 2: Using Algebra 

Student Worksheet 
Teacher Notes 





ii 
iii 

IV 

iv 

V 
V 

VI 


)1-1 1 


1-6 




1-111 


1-18 




1-23 


1-30 




2-1 


2-6 




I 2-10 1 


2-16 



Section 2: Using Algebra 

Student Worksheet 
Teacher Notes 

Chapter 5: Linear Systems 
Section 1 : Using Graphs & Tables 

Student Worksheet 
Teacher Notes 



Tips 



TM 



3-1 



3-6 



3-10 
3-14 



Chapter 3: Linear Functions 
Section 1 : Slope with Grid 

Student Worksheet 
Teacher Notes 

Section 2: Slope Using Coordinates 

Student Worksheet 
Teacher Notes 

Section 3: Slope Rate of Change 

Student Worksheet 
Teacher Notes 

Section 4: Slope-Intercept Form 

Student Worksheet 
Teacher Notes 

Chapter 4: Linear Inequalities: 1 -Variable 
Section 1 : Using Graphs & Tables 

Student Worksheet | 4-1 

Teacher Notes 4-6 



3-18 



3-24 



3-28 



3-33 



4-11 



4-17 



5-1 



5-8 



Section 2: Using Algebra 

Student Worksheet I 5-15 

Teacher Notes 5-28 



1-1 



2-1 



4-1 



5-1 



| Tip™ 1 : Resetting Your Calculator 

| Tip™ 2: Adjusting Your Calculator Settings 

§ Tip™ 3: Graphing a Function in the Standard Window | 3-1 

| Tip™ 4: Creating a Table 

f) Tip™ 5: Adjusting the Viewing Window 

| Tip™ 6: Using Lists IJM 

| Tip™ 7: Creating a Statistical Plot j 7-1 

| Tip™ 8: Finding the Best Line of Fit for a Set of Data 8-1 

§ Tip™ 9: Sending and Receiving Data between Calculators | 9-1 

i Tip™ 10: Managing Your Calculator's Memory |1 0-1 



Introduction to Topics in Algebra 1 




Note to Teachers 

Welcome to the Topics in Algebra 1 software application for the TI-83 Plus and TI-73 graphing 
calculators. The application and Classroom Materials were designed to help students review and 
reinforce selected concepts taught at the Algebra 1 level. Topics in Algebra 1 is easy to use, even 
for inexperienced calculator users, and it encourages students to explore concepts on their own. 

Navigating Topics in Algebra 1 (pages vi-ix) explains how to move around the application. You 
may wish to copy these pages for your students. 

We hope Topics in Algebra 1 proves useful to you and your students. All of your comments and 
suggestions are appreciated. You can contact TI: 



• Phone 

• E-mail 



1-800-TI-CARES (1-800-842-2737) 
ti-cares@ti.com 



TI website education.ti.com 



Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



Organization of Topics in Algebra 1 

Topics in Algebra 1 is organized in textbook fashion with chapters and sections arranged in 
table-of-contents form. 



Chapters 


Sections 


1: Number Sense 


1: Integers 

2: Rational Numbers 

3: Real Numbers 


2: Linear Equations 


1: Using Graphs & Tables 
2: Using Algebra 


3: Linear Functions 


1: Slope with Grid 
2: Slope Using Coordinates 
3: Slope Rate of Change 
4: Slope-Intercept Form 


4: Linear Inequalities: 1-Variable 


1: Using Graphs & Tables 
2: Using Algebra 



Note: Chapters can be installed and deleted individually. This provides flexibility, allowing calculators to have only the applications 
students currently need. 

Each section in the application contains three subsections. 

• The Overview presents definitions and concepts for teachers to use in class discussions and 
for students to use for study and review. They contain animation and real-world examples. 

• The Observations show concepts or examples, followed by Write An Observation screens. 
Students are asked to write in the space provided on the Student Worksheet their 
observations about the content presented. Screens entitled Did you know display additional 
information and facts about the current concept. 

• The Activities include interactive activities that reinforce the concepts covered in the section. 
Many of the activities are in the form of games. Students can practice calculating equations 
with integers, rational numbers, and real numbers, or they can find the equation of a line. The 
application checks answers, gives a score, and provides students with the correct answer if 
they are unable to answer a question correctly. In the Linear Functions chapter, students can 
play a game called Screen Cross where they link to each other's calculators and race to see 
who finishes first. 



Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



Classroom Materials 

The Topics in Algebra 1 Classroom Materials include Student Worksheets, Teacher Notes (with 
answers), and (§) Tips™. 



• 



Student Worksheets provide explanations and instructions to students about using the 
application to review the concepts in the section. Each worksheet is divided into four parts — 
Overview, Observations, Activities (which correspond to the subsections of the application), 
and 1 Try-It!™ on Your TI-83 Plus or TI-73. 

(§ Try-It!™ activities let students investigate specific features on the calculator related to the 
section concepts. This includes step-by-step instructions with the exact keys to press to 
complete each step and corresponding screen pictures. The screens shown in the (§ Try-It! 
activities are for the TI-83 Plus. Usually, the TI-73 display varies only slightly, and the 
students should have no problems following the instructions. However, in the cases where 
the two calculators vary, the fj) Try-It! activities contain two separate exercises, one for each 
of the two calculators. Therefore, you only need to copy the section appropriate for the 
calculator that you use in your classroom. 

Teacher Notes give a brief explanation of the concepts covered in the section, some of the 
common student errors that might be encountered, and answers to the questions on the 
Student Worksheets. There are Teacher Notes for each Student Worksheet. 

fj) Tips™ provide keystroke examples for some of the more common tasks that you and your 
students need for Algebra 1 and beyond. The fj) Tips are intended to help students learn how 
to use the features of the calculator. The fj) Tips topics are: 

fj) Tip 1: Resetting Your Calculator 

fj) Tip 2: Adjusting Your Calculator Settings 

fj) Tip 3: Graphing a Function in the Standard Window 

fj) Tip 4: Creating a Table 

fj) Tip 5: Adjusting the Viewing Window 

fj) Tip 6: Using Lists 

U Tip 7: Creating a Statistical Plot 

(§ Tip 8: Finding the Best Line of Fit for a Set of Data 

fj) Tip 9: Sending and Receiving Data between Calculators 

fj) Tip 10: Managing Your Calculator's Memory 

When students need to learn how to use the feature being covered, you can distribute the 
(!) Tips to them to make sure they are prepared for the lesson. 



Topics in Algebra 1 ©2001 Texas Instruments Introduction 



NCTM Principles and Standards for School Mathematics 

The Topics in Algebra 1 application and the Classroom Materials were written with the 
guidelines of the NCTM Principles and Standards for School Mathematics in mind. Attention 
was paid to the expectations laid out for the Algebra Content Standard for the Algebra 1 level 
that crosses the 6-8 and 9-12 grade bands. 

Some examples include: 



NCTM Standards and Expectations 


On the Application 


To understand patterns, relations, and 
functions. 


Students see how battery voltage values in a 
series can be represented by a linear function. 


To model and solve contextualized problems 
using various representations, such as graphs, 
tables, and equations. 


Students experience how to work with tables of 
values, graphs, and linear equations to see the 
multiple approaches to problem solving. 


To analyze the nature of changes in quantities 
in linear relationships. 


Students determine the constant rate of change of 
a diving submarine along each segment of its dive. 



In addition, scored, interactive activities at the end of each section help reinforce the concepts 
reviewed in the Overview and Observations subsections. 

You can find the complete expectations for the Algebra Content Standard and for the various 
grade bands set out by the NCTM at: 

http://standards.nctm.org/document/appendix/alg.htm 

You can view the NCTM Principles and Standards for School Mathematics online at: 

http ://standards. nctm. org/ 

Acknowledgements 



Texas Instruments 
Sharon Cichocki 
Michael Corrigan 
Cathy Jahr 
John LaMaster 
Brenda Levert 
Nicol Reiner 
Melissa Rowe 
Bill Stiggers 
Bob Tower 



would like to thank these individuals for their support, 
Hamburg High School 
Assumption Catholic School 
Westview High School 

Indiana University-Purdue University Fort Wayne 
Academy for Academics and Arts 
Roosevelt High School 
South Grand Prairie High School 
Cleveland Public Schools 
Roosevelt High School 



ideas, and suggestions. 
Hamburg, NY 
Jacksonville, FL 
Martin, TN 
Fort Wayne, IN 
Huntsville, AL 
Sioux Falls, SD 
Grand Prairie, TX 
Cleveland, OH 
Sioux Falls, SD 



Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



IV 



Installing This Application 

Students may install all four chapters as a unit (ALG1 PRT1) or one or more of the chapters 
individually (ALG1CH1, ALG1CH2, ALG1CH3, ALG1CH4). This provides flexibility, allowing 
calculators to have only the applications students currently need. When two or more chapters are 
installed separately, they each must be accessed directly from the I APPSl menu. 

Installing this application requires TI-GRAPH LINK™ software and link cable. A link cable can be 
purchased from the online store: 

http ://epsstore .ti. com 

If an Archive Full error message appears while installing Algebra 1 or one of the chapters, the 
calculator does not have sufficient memory for the application. Applications and/or archived 
variables must be deleted to make room (see below). 

Deleting an Application 

Deleting an application completely removes the application from the calculator. The space then 
becomes available for a different application. The deleted application may be reloaded at a later 
date. Before deleting an application from the calculator, it can be backed up to a PC using the 
Link > Receive Flash Application menu in TI-GRAPH LINK. You can reload it to the calculator 
later using the Link > Send Flash Software menu in TI-GRAPH LINK. 

To delete an application or archived variable: 

1. Press [2nd] [MEM] to display the MEMORY menu. 

2. Select 2:Mem Mgmt/Del (4:Delete... on the TI-73). 

3. Select A:Apps... or B:AppVars... (8:Apps... or 9:AppVars... on the TI-73). 

4. Press until the ► indicator is next to the item you wish to delete. 



5. Press [DEL] ( \ ENTER] on the TI-73). 

6. Select 2:Yes when asked Are You Sure? 

7. Press 1 2nd I [QUIT] to return to the Home screen. 



Topics in Algebra 1 © 2001 Texas Instruments Introduction 



Navigating Topics in Algebra 1 

Starting the Application 

1. Press IAPPSI to display the APPLICATIONS menu. 



2. Press until ALG1 PRT1 (or a chapter such as ALG1 CH1) is highlighted, and then press jEMTERj to 
select it. The application title page is displayed. 



X* TEXAS 
TirlHSTfiUmHTS 



TURKS IR ALGEBRA i 



* PRESS fltlV KEV Tn i£*nT} 
^2001 TEKAS IRSTRUHERTS 



-Topics in Algebra 1 title page 



3. Press any key to start the application. 

A Table of Contents page is displayed. It is the Table of Contents from which you last exited 
Algebra 1. You may select one of the items on the menu or press (UP) as often as necessary to go 
to the Table of Contents screen that you need. 

Table of Contents Screens 

There are three types of Table of Contents screens — chapters, sections, and subsections. 



HlfcH3ftH!MiH*« 

FtlnUHBER SEhSE ~1 
2:LinEflREQUflTinnS L- 

j: LinEHF; FuriLTinn; 

H:LIREARIREQ:i-YAR — ' 
fEKITl (fiELPl 







Algebra Chapters 



Note: If you have installed the 
chapters individually, only the current 
chapter is shown on this screen. 
Press I enter | to select the chapter. 



When you select a chapter, the Algebra Sections screen is displayed. The number of sections 
listed varies according to chapter. 



PI 
lnnuH 



EIMEgBil 



RUHBER SERSE 



PfllRTEGERS 
2:RATinAAL AUHBERS 
3: REAL AUHBERS 



3 



> 



fEKITl fuFl fHELPl 



Algebra Sections 



When you select a section, the Algebra Subsections screen is displayed. The items listed are always 
the same — Overview, Observations, and Activities. 



ALGEBRA SUBSECTIDriS 



1: DUMBER SERSE 



INTEGERS 



FflDUERUIEU 

2:DBSERURTIDnS 

J:HCTIVITIES 



> 

fEKITl fuFl fHEL?| 



Algebra Subsections 



Note: When you exit and re-enter Topics in Algebra 1 , you return to the Table of Contents screen from which you exited. 



Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



VI 



Navigating Topics in Algebra 1 (continued) 

Selecting the Chapter, Section, and Subsection You Want 

To select from a Table of Contents screen, press if necessary to highlight the name of the 
chapter, section, or subsection, and then press IENTERI . 



■■IMMflMIMH 

i:MJHBERSEnSE 

£: LiriEflF; EQUflTinrii" 

EBLiriEHF; FuriLTinn; 

H: LiriEflF; niEQ: l-'.'HF; 



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(HelFi 



[T^n 



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LiriEHF; FUmiTinriL" 



a 



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j: jLnFE rhte nF CHHriuE 

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fEKITl fuFl (fiELPl 




LiriEHF; FuriLTinn; 




jLnpE ujim; cddrd 

DVERVIEU 



When the Overview, Observations, or Activities opening screen appears, press |T) to begin. 

Returning to the Table of Contents 

From most Overview, Observations, or Activities screens, you can press 1 2nd I [QUIT] as many times 
as necessary to return to the Table of Contents. You may then select one of the items on the 
menu or press (UP) to go to higher levels of the Table of Contents. 

Note: If you see (CONT) on the current screen, you must first press any key to continue. 

Leaving the Application 

To leave the application, press 1 2nd I [QUIT] as many times as needed to return to a Table of 
Contents screen, and then press (EXIT). When you re-enter the application, you return to this 
Table of Contents screen. 



Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



VII 



Navigating Topics in Algebra 1 (continued) 
Navigation Star 

The navigation star is located on the bottom right of most Overview and Observations screens. 

When the right and left arrows of the navigation star are flashing, press |T| and \±\ on the 
calculator to page back and forward between screens. When the up and down arrows are 
flashing, and are used to navigate vertical menus (see below). 



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riMTUF;HL: [i..l..;:..H ...I 



HHQLE 



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inTEGER: Z...-Z/-I/Q/I1Z ...J 



Press (TJ to display the 
next screen. 

► 



-Navigation star 



THE SIGn DF H MJHBER 



TELLS YDU THE DIRECTIDn 
DFTHE MJHBER FftDH ZERO 



i l I I I I I I I D 
-H "5 "E "i 1 E 5 1 



Horizontal Menus 

A horizontal menu may be displayed at the bottom of the screen. The menu items help you move 
between screens in the application. The menu items change from one screen to another. The 
following are the most frequently displayed menu items. 



Menu Item 


Press 


To Do This 


(EXIT) 


m 


Exit the application. 


(UP) 




Move up a level in the menu structure. 


IZOOMI 


(HELP) 




Display the HELP MENU. 


IGRAPHI 


(MAIN) 


m 


Return to the previous screen from the HELP MENU. 


(BACK) 




Return to the HELP MENU from a HELP explanation screen. 


IWINDOWI 


(MENU) 


m 


Return to the previous menu screen. 


(QUIT) 


m 


Quit an activity. 



To select a menu item, press the calculator key that corresponds to the menu item on the screen. 



Horizontal 
menu 



4 



ALGEBRA SUBSECTinnS 



i: MJHBER iETliE 



i: INTEGERS 



ran'.'Efi'.'IEM 
2:DB£ERUATIDR£ 
3: ACTIVITIES 

(EKffi nrn ihelti 



O [ZOOMl IGRAPHI 



These menu items 
map to 
-these calculator keys. * 



* In these materials, the items 
in the horizontal menus are 
shown in angle brackets; for 
example (EXIT), (UP), and 
(HELP). 

The menu items change 
from one screen to another. 
On some screens, different 
menu items are mapped to 
the calculator keys. 



Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



VIM 



Navigating Topics in Algebra 1 (continued) 

Vertical Menus 

When the up and down arrows of the navigation star are flashing, press and on the 
calculator to highlight an item in a vertical menu. 



Vertical menu 

First item is highlighted. 



■HHiaEJI^H 
sdldtidr search 
dsirg rdhper lire 

4 r-g * 

-i > 



4- 



SELECT £ PRESS [ERTER] O 



As you press Q and to move 
through the menu, additional 
information is displayed to the 
right of the menu. 



Some vertical menus only provide information. Other vertical menus are used for navigation. If 
Select or Select & Press [Enter] is displayed, you can press I ENTER I to select an item or to see more 
information. 



SDLUTIDR SEARCH 
«_^| DSIRG A TABLE 



4 


Hx 
H 
B 
12 



SELECT £ PRESS [ERTER] 




Press | ENTER | to select the 
second item on the vertical 
menu and display the first 
in a sequence of screens 
for this selection. 

Press (MENU) (0) to 
return to the menu screen. 



FIRD THE SDLUTIDR SET 



0+2 J 1 



+H 1 1 1 1 1 h+ 

-3 - 2 "10 12 3 
IfiERUl 



(CONT) 

When you see (CONT) (continue), you can press any key to go to the next screen. 





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HELP 

From a Table of Contents screen, press (HELP) to view information about features of the 
application. To select an item, press to highlight it, and then press I ENTER I . 



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Topics in Algebra 1 



©2001 Texas Instruments 



Introduction 



IX 



Chapter 1 : Number Sense 
Section 1 : Integers 



Name 
Date 



Number Sense: Integers 



Overview 




Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate number sense concepts relating to the set of integers. Scroll through 
the Observations using (T| ([JJ to review, if necessary). Read each screen carefully. When you 
come to a Write an Observation screen, stop and write the answers to the questions on your 
worksheet. 



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HDU FflF; ARE 

THEV RPRRT? HO 

USE YUUR HURKSHEET. 



£0 



Observation 1 

How far apart are the bird and the fish? Should your answer be 
positive or negative? Write an explanation for your answers here. 



HRITE Rn DBSERYRTinn . 



IF YDU MULTIPLY TUD 

NEGATIVE RUBBERS: 

"3 * -ii 

UHRT If THE SIGR DF 
THE ARSHER? 

USE YDUR HURKSHEET. 



Observation 2 

What is the sign of the answer to the problem -3 x -11? 



In your own words, state the rules for multiplying and dividing 
signed numbers (shown in the grids on the next screens). 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-1 



Chapter 1 : Number Sense 
Section 1 : Integers 



Name 
Date 



Activities 

The Activities help you practice integer concepts. You can select from two different activities — 
What Is My Sign? and Integer Smash. Follow these steps to play the activity and complete your 
worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press [ENTER]. 



SELECT fln ACTIVITY 



j5 



1. HHflT IS HY SIC-R ? 



USE THE RRRDU KEYS 
TD SLIDE THE 
EXPRESSIDH TD THE 
CDRRECT SIGR. 



SELECT £ PRESS [ERTER] O 



Scoring: Every correct 
response earns 2 points. 

The game automatically 
ends if you have 
answered incorrectly four 
times (shown in the top 
right corner), or you press 
(QUIT) to stop. 



What Is My Sign? 

1. In your head, quickly solve the sliding expression to 
determine if the result is positive, negative, or zero. 

2. As soon as you know the sign of the result, press and to 
move the expression into the proper category on the left 

(+, 0, or -). Once the expression is in the correct row, you can 
press to slide it quickly to the left. If the answer is 
incorrect, the correct answer is displayed; press any key to 
resume play. 

3. Follow your teacher's instructions for how long to play the 
activity. 

4. What was your score? 



5. How many incorrect answers did you have? 

(Shown in top right corner of the screen.) 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1 -2 



Chapter 1 : Number Sense 
Section 1 : Integers 



Name 
Date 



Activities (continued) 





| SELECT An ACTIVITY | 


El 




■MI- 


2. INTEGER SMASH 






FIRD THE 
HISSIRG RUBBER. 


SELECT i. PRESS [ERTER] 


O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 



Integer Smash 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press jEMTERj to select it. 

2. For bronze or silver levels only, press (+), (-), (*}, or (-=-) to 
select the operation you want to practice. 

3. Enter the missing number (press O for negative numbers) 
and press IENTERI . If the answer is incorrect on the second 
attempt, the correct answer is displayed; press any key to 
resume play. As you play the activity, write each number 
sentence and solution. Show your work here. 



4. What level and operation (bronze and silver only) did you 
play? 

5. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1 -3 



Chapter 1 : Number Sense 
Section 1 : Integers 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Learn to use the subtraction key (B), the negation key (O), and the absolute value function 
(abs(). 

Use the negation and the subtraction keys to calculate _ 5 - -4. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Calculate "5 - -4. 

Note: The negation key (\H\) and the subtraction key 
(B) are different. 


B5B04 
I ENTER | 










-5- -4 

-1 





Enter _ 5 - ~3 x -2, first without using parentheses and then using parentheses. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Calculate "5 - "3 x -2. 

Note: On the TI-73, notice the difference between 
the x variable key (\x\) and the multiplication 
key (0). 


e 5 b e 3 s B2 

I ENTER | 










-5- -4 

-1 
-5- -3* -2 

-11 




2. Calculate "5 - ("3 x -2). 


B5B 
B03B02B 

| ENTER | 










-5- -4 

-1 
-5- -3* -2 

-11 
-5-C-3*-2> 

-11 










3. Calculate ("5 - -3) x -2. 


BB5BB3B 
EB2 

I ENTER | 










-1 
-5- -3* -2 

-11 
-5-C-3*-2> 

-11 
C-5--3>*-2 

4 











The calculator uses the Order of Operations rules, which say that multiplication and division are 
performed from left to right, and then addition and subtraction are performed from left to right. 
Notice that multiplication was calculated before subtraction in the expression _ 5 - ~3 x _ 2. Notice 
that the expression _ 5 - ("3 x _ 2) has the same answer. 

The calculator performs operations inside the parentheses before operations outside the 
parentheses. Notice that the expression ( - 5 - "3) x _ 2 has a different answer than the expressions 
-5 - -3 x -2 and "5 - ("3 x -2). 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1 -4 



Chapter 1 : Number Sense 
Section 1 : Integers 



Name 
Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Use the absolute value (abs() function on the calculator to find the absolute value of "12. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Find the absolute value of "12, which 
is written as l"12 1. 

Note: The |math| NUM menu varies slightly from the 
TI-73 to the TI-83 Plus. 












|MATH| Lll 




MRTH IJllii CPX 
(HabsC 
2: round < 
3: iPartC 
4: f PartC 
5: intC 
6:nint 
7-1-naxt 


PRB 












2. Select the absolute value (abs() 
function. It is copied to the Home 
screen. 


1 :abs( 












-5- -3* -2 
-5-C-3*-2> 
C-5--3>*-2 
absC 


-1 

-11 

-11 

4 












3. Calculate the result. 


B12Q] 

I ENTER | 












-5-C-3*-2> 
C-5--3>*-2 
absC-12> 


-11 

-11 

4 

12 













Additional problems — Calculate the following problems by hand, then check your answers 
using the calculator. Remember to use the Order of Operations rules. 



1. 



-4 + -12 x -10 



2. 



4x-8--10x2 = 



-30 + -5 - 6 = 



4. I -12 +-28 I = 



I -4 x -8 - -10 x 2 I = 



■I -3 -14 --10 I = 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1 -5 



Chapter 1 : Number Sense 



Section 1 : Integers 



Number Sense: Integers 




Teacher Notes 



Objectives 

• To illustrate the set of integers in a Venn diagram. 

• To give an overview of the following definitions: the sign of a number, numbers of opposite 
sign, and absolute value. 

• To give illustrations of the sets of positive and negative integers, and zero. 

• To review ordering and the additive inverse property. 

• To show examples of addition, subtraction, multiplication, and division of integers. 

Math Highlights 

This section begins with a Venn diagram and follows with an illustration of the use of integers on 
the Fahrenheit and Celsius scales. The temperature equivalencies shown are integer values. 
Students are reminded that the absolute value operation is defined as the distance of the number 
from zero. Examples of addition, subtraction, multiplication, and division operations are given. A 
number line model is used for addition and subtraction. Subtraction uses the add-the-opposite 
rule. 

Common Student Errors 

Students may have trouble identifying rules, such as the add-the-opposite rule for subtraction. 

Note: The number line model for addition and subtraction is shown on the calculator when the Topics in Algebra 1 application is 
installed. 

Following are some activities to help students construct the rules for multiplication and division. 
These activities are not part of the Topics in Algebra 1 application. 



Pattern Development for Multiplication and Division 



Investigation 1 : What is the product of a positive and negative 
number? 

Begin by writing the product of two positive numbers, for example, 
3x3 = 9. Keep decreasing the second term by 1 to create the sequence 
of multiplication values shown to the right. Notice the values on the 
right side of the number sentences decrease by 3. 

Observation: The product of a positive and negative number is 
negative. 



3x3= 9 

3x2= 6 

3x1 = 

3x0 = 

3x-l = 

3x-2 = 

3x-3 = 



3 




Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-6 



Chapter 1 : Number Sense 



Section 1 : Integers 



Common Student Errors (continued) 



Pattern Development for Multiplication and Division (continued) 



Investigation 2: What is the product of two negative numbers? 



-9). 



Start with the last number sentence from Investigation 1 (3 x -3 
Keep decreasing the first term by 1 to create the sequence of 
multiplication values shown to the right. Notice that the values on the 
right side of the number sentences increase by 3. 

Observation: The product of two negative numbers is positive. 



3 x -3 = -9 
2 x -3 = -6 
1 x -3 = -3 
x -3 = 
-lx-3= 3 
-2 x -3 = 6 
-3x-3= 9 



Investigation 3: What are the division rules for multiplying signed 
numbers? 

Observation: Division rules are developed using multiplication as the 
inverse operation. The rules are similar. 



-6-5-3 

3x-2 



-2 since 
-6 



■6 -f- - 2 = 3 since 
-2x3= -6 



Sti 



Student Worksheet Notes with Answers 



Overview 

Tell students: 

1. How to find the Overview, if necessary. 

2. How to navigate the application, if necessary. 




3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-7 



Chapter 1 : Number Sense 



Section 1 : Integers 



Observations 

The Observations help students understand operations with signed integers. If necessary, tell 
students how to find the Observations. 



HRITE An UBSERVATIUn . 



► SO 



HDU FAR ARE 
THEV APART? hO 
USE YDUR UDRHSHEET. 



-75 



Students see the answers 
on the following three 
screens. 



EHHaiEEaMHMl 

IF YDU MULTIPLY TUD 

NEGATIVE MJHBERS: 

"3 * -ii 

UHAT IS THE SIGA DF 
THE AASHER? 

USE YUUR HURKSHEET. 



Students see grids 
explaining the rules. 



Observation 1 

How far apart are the bird and the fish? Should the answer be 
positive or negative? Students write an explanation of their 
answers. 

The bird and the fish are +125 ft. apart. The distance is 
positive. (Students will see the answers on the next three 
screens. Signed numbers give a perspective as shown on the 
screens.} Explanations will vary. 



liHil'JilllihH**] 



-75-50= -125 
THE FISH IS v 
1E5 ft BELDU «1"^ 
THE BIRD 

OR... * 



► 50 



■75 



MMUJ.III.iadU 




50—75= +125 
THE BIRD IS v 
1E5 ft ABOVE k^-w 
THE FISH 

OR... * 


+50 


-75 

O 



Majuj.m.iadu 




THE BIRD AAD V 
THE FISH ,- 
ARE 125 ft 
APART ! ^ 


+50 


-75 

O 



Observation 2 

What is the sign of the answer to the problem _ 3 x -11? 
The answer is positive. S x -11 = 33. 



mmsMEEMm 

MULTIPLY UR DIVIDE 

+ - 
+ 



+ _ 
+ 



SAME SIGflS -*■ PUSITIVE 



MULTIPLY DR DIVIDE 

+ - 
+ 



UPPUSITE 
SIGAS 



-* AEGATIVE 



What are the rules for multiplying and dividing signed numbers? 
The product of a positive and negative number is negative. 
The product of two numbers with the same sign is positive. 
Rules for division are similar to the rules for multiplication. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-8 



Chapter 1 : Number Sense 



Section 1 : Integers 



Activities 



SELECT fln ACTIVITY 



j5 



1. HHflT IS HY SIC-R ? 



USE THE RRRDU KEYS 
TD SLIDE THE 
EKPRESSinR TD THE 
CDRRECT SIC-R. 



SELECT £ PRESS [ERTER] O 



Scoring: Students earn 2 
points for each correct 
response. 

Unless you specify point 
or time limits for this 
activity, students can play 
the activity until they have 
answered incorrectly four 
times or they press 
(QUIT) to stop. There is 
no time limit. 



rat 



aaEUHBH 



2. INTEGER SHRSH 



FiriD THE 
HISSIRG RUHP-ER. 



SELECT £ PRESS [ERTER] O 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

Students can earn up to 
10 points. 

Tip: You may want to 
remind students playing 
at the gold level about the 
Order of Operations rules. 



What Is My Sign? 

Tell students to: 

1. Quickly solve the expression in their heads before it slides all 
the way to the left. 

2. Move the expression into the correct category (+, 0, or -) using 
and 0- Once the expression is in the correct row, they can 
press [JJ to slide it quickly to the left. If the answer is incorrect, 
the correct answer is displayed; press any key to resume play. 

3. Follow your instructions. For example, students can play: 

• Until they have answered incorrectly four times (no time 
limit). 

• Until a certain amount of time has expired (highest score 
with the fewest misses wins). 

• Until a certain score has been reached (first student to 
reach the score with the fewest misses wins). 

• Repeatedly over a period of time (days, weeks, etc.) for 
tracking improvement of high scores. 

4. Record their score. 

5. Record how many incorrect answers they had. 

(Shown in top right corner of the screen.) 

Integer Smash 

Tell students to: 

1. Highlight a level (bronze = least difficult; gold = most difficult), 
and press IENTERI to select it. 

2. Bronze or silver levels only: Press (+), (-), (*), or (-=-) to select 
the operation that they want to practice. 

3. Enter the missing number (press O for negative numbers) and 
press IENTERI . As they play the activity, write each number 
sentence and solution, showing all of their work on the 
worksheet. 

4. Record the level and operation (bronze and silver only) they 
played. 

5. Record their score. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-9 



Chapter 1 : Number Sense Section 1 : Integers 



1 Try-It!™ on Your TI-83 Plus or TI-73 

These keystroke exercises let students practice using the basic operation keys (EL 0, EL ED, the 
negation key (ED), the parentheses keys (Q] Q]), and the absolute value function ( 1 MATH I NUM 
1 :abs( ). 

Tell students to follow the steps exactly on the calculators. Example screens are displayed on 
the worksheets for students to compare with the calculator screens. 

Additional problems — These problems give students additional practice using the subtraction 
key (El), the negation key (ED), and the absolute value function ( I MATH I NUM 1 :abs( ). Remind 
them to follow the Order of Operations rules. 

Tell students to do the following calculations by hand, and then check the answers using the 
calculator. 

1. -4 + -12 x -10 = 116 2. 4x-8--10x2 = -12 

3. -30--5-6 = 4. I -12 +-28 I =40 

5. I -4 x-8- -10x2 I = 52 6. -I -3 - 14 - -10 I =-7 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 1-10 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



Number Sense: Rational Numbers 




Student Worksheet 



Overview 

The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate number sense concepts relating to rational numbers. Scroll through 
the Observations using (T| ([JJ to review, if necessary). Read each screen carefully. When you 
come to a Write an Observation screen, stop and write the answers to the questions on your 
worksheet. 



■!lft««IJ.HH«Miiim 

HRITE l| lil" An 

IMPROPER FRACTIUR. 
USE VnUF; WORKSHEET. 



Observation 1 



Write 4 — as an improper fraction. 

Write your answer here. Show all of your work. 



URITE Rn DBSERYRTinn . 



WRITE | RRD ^- 

AS DECIMALS. 

USE YDUR UURKSHEET. 



Observation 2 

5 2 

Write - and — as decimals. 
8 11 

Write your answer here. Show all of your work. 



URITE AU ORSERVATIOn . 



URITE .1B7S liriD ^ 



AS PERCENTAGES. 
USE YOUR UURKSHEET. 



Observation 3 



Write .1875 and — as percentages. 

Write your answer here. Show all of your work. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-11 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



Activities 

The Activities help you practice rational number concepts. You can select from two activities — 
Slide and Number Smash. Follow these steps to play the activity and complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and then press [ENTER]. 



SELECT fln ACTIVITY 



j5 



1. SLIDE I 



USE THE ARRDU KEYS 
TD LITlE UP THE 
FRACTIDRS SD THEY 
ADD TD i. 



SELECT £ PRESS [EDTER] O 



Scoring: When a row or 
column adds up to 1 , it 
disappears, and you 
score 2 points. 

The game automatically 
ends if the screen is full 
or if you press (QUIT) to 
stop. 



Slide 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press IENTERI to select it. 

2. Line up the fractions so they add to 1 (horizontally or 
vertically). As a fraction slides across the screen, press and 
to move it up or down. Once a fraction is in the correct 
row, you can press to slide it quickly to the left. 

3. Follow your teacher's instructions for how long to play the 
activity. 



4. What level did you play? 

5. What was your score? 



6. 



Write a paragraph describing the Slide activity. What was your 
strategy for playing the game? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-12 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



Activities (continued) 





| SELECT An ACTIVITY | 


El 




■MI- 


2. RUHBER SMASH 






FIRD THE 
HISSIRG MJHBER. 


SELECT i. PRESS [ERTER] 


O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 

Tip: To change an 
answer before you press 
Ienteri , press Icleari and 
re-enter the answer. 

Tip: Press <n/d> to move 
between the numerator 
and denominator. 



Number Smash 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press IENTERI to select it. 

2. Press (+), (-), (*>, or (■=■) to select the operation you want to 
practice. 

3. Enter the missing number (press O for negative numbers), 
and press IENTERI . As you play the activity, write each number 
sentence and solution. Show your work below. 

• To enter a mixed number, enter the whole number and 
press (UNIT). Then enter the fraction. 

• To enter a fraction, press (n/d) and enter the numerator. 
Press (n/d) again and enter the denominator. 

If the answer is incorrect, the correct answer is displayed; 
press any key to resume play. 



4. What level and operation did you play? 

5. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-13 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus 

2 5 
Investigate how the calculator computes addition expressions. Solve — + — 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)ICLEARI 


2. Enter the expression on the Home 
screen. 


2030506 










2^3+5^6 




3. To specify that you would like the 
result to be shown in fraction form, 
select ►Frac. It is copied to the Home 
screen. 










|MATH| 
1 >Frac 




jjUK HUM CPX PRB 

flHHFrac 

2: ►Dec 

3:3 

4:3J"< 

5; x j~ 

6:fMin< 

7-i-fMaxC 










4. Evaluate the answer. 










| ENTER | 




2/3+5/6 ►Frac 

3/2 





Notice that the answer is in simplified form. The calculator follows the Order of Operations 
rules. Division is performed before addition. Solve this problem by hand. Show all of your work. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-14 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



Try-It!™ on Your TI-83 Plus (continued) 



Investigate how the calculator computes division expressions. Solve 



1 ^2 

2 '3 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Solve without parentheses and 
specify that you want the result in 
fraction form. 


1020203 
| MATH 1 1*Frac 
I ENTER | 










1/2/2/3 ►Frac 

1/12 

I 




2. Solve using parentheses and specify 
that you want the result in fraction 
form. 


010200 
02030 
| MATH 1 1*Frac 
I ENTER | 










1/2/2/3 >Frac 

1/12 
a/2VC2/3^Frac 

3/4 

I 





The calculator gives two different answers, depending on how you entered the expression. 

1 2 
Which one is the answer for the problem — -f — ? 

2 3 

Solve this problem by hand. Show all of your work here. Explain which answer from the 
calculator is the desired answer and why. 



Additional problems — Calculate the following problems by hand. Simplify your answers. Then 
check your answers using the calculator. Remember to use the Order of Operation rules. 



1 1 

3 + 4" 



— x — 
3 6 



3. — * — 



3 5 
5" 6 



1 -2 

2~ 5 



4. = 



2 1 2 

— + — x — 
5 4 3 



1 3 1 
8 * 16 " 2 



7. 



1 1 3 
6 12 + 4 



1 3 

+ (-3) 

2 4 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-15 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



1 Try-It!™ on Your TI-73 

2 5 
Investigate how the calculator computes addition expressions. Solve — + — 



To Do This 


Press 


Display (Ti-73 shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Select the b/c and Mansimp mode 
settings. 

Note: See | Tip™ 2: Adjusting Your Calculator 
Settings for more information. 


|M0DE| 

SEEBto highlight 
b/c 












r.0 123456789 
S Radian 




ftufo' 

Flute 


■c [SHE 


isinp IBEIB3IDI3 


IENTERI 

to highlight 

Mansimp 

IENTERI 










3. Calculate the result. 


[2nd] [QUIT] 
21300 
5 [Ml 6 IENTERI 














4. Simplify the fraction. 










ISIMPI IENTERI 


|>sinp y j-*\ 

Simplified by &/ 
factor of 3. 





Notice that the answer is in simplified form. The calculator follows the Order of Operations 
rules. Division is performed before addition. Solve this problem by hand. Show all of your work. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-16 



Chapter 1 : Number Sense 
Section 2: Rational Numbers 



Name 
Date 



Try-It!™ on Your TI-73 (continued) 



Investigate how the calculator computes division expressions. Solve 



1^2 

2 ' 3 



To Do This 


Press 


Display (TI-73 shown) 


1. Solve without parentheses and 
specify that you want the result in 
fraction form. 


10 20 20 3 
I PHD 1 1 ENTER | 










12 

I 




2. Solve using parentheses and specify 
that you want the result in fraction 
form. 


E]10 2 Q] ED 
[Q20 3 Q] 
|F«»D||ENTER| 










1/2/2/3 ►F**D L 
a/2VC2/3^F^D 

■^ioo 

I 




3. Simplify the result by a factor of 25. 


|SIMP| 25 










1/2/2/3 ►R--MD L 

<l/2>/<2/3>^F*-+D 

+ ioo 
Hi^SinP 25 ^ 











The calculator gives two different answers, depending on how you entered the expression. 
Which one is the answer for the problem: 

1 ^2 
2~"3~ 

Solve this problem by hand. Show all of your work here. Explain which answer from the 
calculator is the desired answer and why. 



Additional problems — Calculate the following problems by hand. Simplify your answers. Then 
check your answers using the calculator. Remember to use the Order of Operation rules. 



1 1 

1. "- + -: 

3 4 



2 5 
2. --X-- 

3 6 



3 5 
5" 6 



1 -2 
2 _ 5 



— + — X — : 

5 4 3 



1 



1 



6. - X — -r — = 

8 16 2 



1 1 3 

7. + — 

6 12 4 



8. 



1 3 

2~ 4 



(-3) 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-17 



Chapter 1 : Number Sense Section 2: Rational Numbers 




Number Sense: Rational Numbers Teacher Notes 

Objectives 

• To review the definition of rational numbers as ratios and as terminating and repeating 
decimals. 

• To review ordering and the reciprocal property of rational numbers. 

• To review operations with rational numbers. 

Math Highlights 

Students review rational numbers. This includes rational numbers as ratios, terminating 
decimals, repeating decimals, and integers, as well as operations with fractions. In the 
Observations, students are reminded of the connection between fractions, decimals, and 
percents. 

Common Student Errors 



• 



Students might confuse the algorithms for addition, subtraction, multiplication, and division 
of fractions. 



• Students may have trouble identifying whether a fraction is positive or negative. For 
example: 



I 


I 




I 


-1 


1 


3 " 


3 


or 


-3 " 


3 " 


3 



• 



Students may have problems because they use short cuts to change the decimal 
representation of a number to a percent representation. Using short cuts does not provide an 
understanding of why the representations are equal. Students should understand that the 
quantity stays the same. Using the multiplicative identity, 1=100/100, is the key to the change 
in the representation. For example, students change . 1875 to a percent. A shift of the decimal 
point gives the correct answer, but without any connection to the math they know. However, 
multiplying by 1 in the form 100/100 gives the same result and makes the connection to the 
math as well. 

100 18.75 

.1875 x = = 18.75% 

100 100 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 1-18 



Chapter 1 : Number Sense 



Section 2: Rational Numbers 




Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand number sense concepts relating to rational numbers. 
If necessary, tell students how to find the Observations. 



■!lft««IJ.HH«Miiim 

HRITE l| lil" An 

IMPROPER FRRCTinn. 
USE YDUR WORKSHEET. 



Observation 1 



Write 4— as an improper fraction. 



Answer: 



14 



Remind students to write the answer on the worksheet and to 
show all of their work. 



Students see the answer 
on the next two screens. 
Tell students to check the 
answers on the 
worksheet. 



h| = M HIKED riUMEEF;.. 
Clin RE URITTEn ML" 
H FRHCTIDn ... 





■Mm 






-! 


-H 






=T*H 






= ¥♦!= 


in 

3 


O 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-19 



Chapter 1 : Number Sense 



Section 2: Rational Numbers 



Observations (continued) 



HRITE AA DBSERYATIDA . 



WRITE I AAD jj- 

AS DECIMALS. 

USE YDUR UDRKSHEET. 



Observation 2 

5 2 

Write - and — as decimals. 

8 11 

Answer: .625 and .18. 



Activities 



Remind students to write the answers on the worksheet and to 
show all of their work. 



Students see the answers 
on the next two screens. 
Tell students to check the 
answers on the 
worksheet. 



DID YOU KRDU . 



A FRACTIDA IS CHARGED TD 
A DECIMAL BY DIYIDIRG : 



1=5- 



■ SEE 
~* HJS.000 



£=.fi2£ 



TERHIRATIAG 
DECIMAL 



DID YDU KRDU . 



A FRACTIDR IS CHARGED TD 
A DECIMAL BY DIYIDIRG : 



1 .lfllfl.. 

11 = 2^11-* iiJZ.0000 



2 rs REPEATIAG 
If" DECIHAL 



■!i*««ia.iwjMHiiim 

HRITE .1B7S ARD ^ 

AS PERCERTAGES. 
USE YDUR UDRHSHEET. 



Observation 3 



Write .1875 and — as percentages. 

Answer: 18.75% and 25%. 



Remind students to write the answers on the worksheet and to 
show all of their work. 



Students see the answers 
on the next two screens. 
Tell students to check the 
answers on the 
worksheet. 



.1B7S = i.Z.?SV. 

WHY? — * O 




A DECIMAL IS CHARGED TD A 
PERCERT BY HULTIPLYIRG 


BY II1IHIIDBIIDBI 


1H7 r *^ - iS^" IB 71V 

1B?E *ioo ■ ioo ■ 1B7S * 


i = .2S^.2S*i00^. = 2S^.^ 






EaaaaHH 



■ SLIDE I 



USE THE ARRDU HEYS 
TD LIRE UP THE 
FRACTIDRS SD THEY 
ADD TD 1. 



SELECT & PRESS [ERTER] O 



Scoring: When a row or 
column adds up to 1 , it 
disappears, and the player 
scores 2 points. 

The game automatically 
ends if the screen is full, 
or you press (QUIT) to 
stop. 



Slide 

Tell students to: 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press IENTERI to select it. 

2. Line up the fractions so they add to 1 (horizontally or 
vertically). As a fraction slides across the screen, press and 
to move it up or down. Once a fraction is in the correct 
row, they can press |T| to slide it quickly to the left. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-20 



Chapter 1 : Number Sense 



Section 2: Rational Numbers 



Activities (continued) 



j5 



EfflEEHHH 



1. SLIDE I 



USE THE ARRDU KEYS 
TDLITlE UP THE 

frrctidrs sn they 

HDD TD i. 



SELECT & PRESS [EHTER] O 



Scoring: When a row or 
column adds up to 1 , it 
disappears, and the player 
scores 2 points. 

The game automatically 
ends if the screen is full, 
or you press (QUIT) to 
stop. 



Slide (continued) 

3. Follow your instructions. For example, students can play: 

• Until the screen fills up (no time limit). 

• Until a certain amount of time has expired (highest score 
wins). 

• Until a certain score has been reached (first student to 
reach the score wins). 

• Repeatedly over a period of time (days, weeks, etc.) for 
tracking improvement of high scores. 

4. Record the level they played. 

5. Record their scores. 





| SELECT Rll ACTIVITY | 


El 




■ar 


2. RUHBER SHASH 






FIRD THE 
HISSIRG MJHBER. 


SELEC 


T i. PRESS [ERTER] 


O 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

They can earn up to 10 
points. 

Tips: Tell students that 
they can: 

• Change the answer 
before they press 
lENTERj by pressing 
ICLEARI and re-entering 
the answer. 

• Press (n/d) to move 
between the numerator 
and denominator. 

Note: Unsimplified 
fractions are counted as 
correct. 



6. Write on the worksheet a paragraph in which they describe 
the Slide activity and the strategy for playing. 

Number Smash 

Tell students to: 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press lENTERj to select it. 

2. Press (+), <-), (*>, or (-=-) to select the operation that they want 
to practice. 

3. Enter the missing number (press O for negative numbers), 
and press jEMTERl . As they play the activity, they should write 
each number sentence and its solution on the worksheet, 
showing all their work. If the missing number is a mixed 
number or fraction, tell them: 

• To enter a mixed number, enter the whole number, press 
(UNIT), and then enter the fraction. 

• To enter a fraction, press (n/d) and enter the numerator. 
Press (n/d) again and enter the denominator. 

If the answer is incorrect, the correct answer is displayed; 
press any key to resume play. 

4. Record the level and operation they played. 

5. Record their scores. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-21 



Chapter 1 : Number Sense Section 2: Rational Numbers 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Review the Order of Operations rules with students, if necessary. Explain to them that the 
calculator uses the Order of Operations rules to simplify expressions. Discuss with them how 
parentheses are used. 

Note: The § Try-It! activities are repeated for each of the two calculators — the TI-83 Plus and then the TI-73. The problems are the 
same, but they vary due to the differences in the two calculators. The Additional problems, which are identical, can be performed on 
either calculator. They are repeated for your convenience when you copy the activities. 

Tell students to do the two calculator fj) Try-It! investigations. 

2 5 

• Investigate how the calculator computes addition expressions. Solve — + — . 

1 2 

• Investigate how the calculator computes division expressions. Solve — -r — . 

Ask students to explain the difference in the two results in second investigation. 

Although each of the two results is correct based on how the problem was entered, to make sure 
that the division is performed correctly, the problem must be entered as (1 / 2) / (2 / 3). The 
answer is 3/4, not 1/12. The calculator uses the Order of Operations rules. Operations inside 
parentheses are performed before operations outside parentheses. 

On the TI-73, students must simplify the fraction 75/100 to get 3/4. They may either specify the 
factor to use, as shown, or let the calculator simplify the fraction, one factor at a time by 
repeatedly pressing ISIMPl . 

Additional problems — Make sure that students understand and use the Order of Operation 
rules so they can determine when to use parentheses. 

Ill 255 

3 + 4 ~ 12 

3 5 18 
5 " 6 " 25 

2 12 7 
5. " — + — x — = - — 

5 4 3 30 

113 1 13 1 

7. + — = - 8. -(-3) = -- 

6 12 4 2 2 4 4 



z. 


3 6 9 




1 -2 9 


4. 


2 " 5 " 10 




13 13 


b. 


8 16 2 64 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 1-22 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



Number Sense: Real Numbers 



Overview 




Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate number sense concepts relating to real numbers. Scroll through the 
Observations using \T\ ([JJ to review, if necessary). Read each screen carefully. When you come 
to a Write an Observation screen, stop and write the answers to the questions on your worksheet. 



HRITE fln DBSERYRTIDn . 



HRITE THREE DIFFERENT 
IRRflTIDRflL RUBBERS. 



USE YDUR UDRKSHEET. 



Observation 1 

Write three different irrational numbers. Show your work. 



TRY THESE PRDBLEHS . 
USE YDUR UDRKSHEET. 



H*i02 : 
b+Hb = 



Observation 2 

Try these problems . . . 

Use the real number properties to solve the following problems 
quickly. Show your work. 



25 x 24 = 



8 x 102 = 



6x46 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-23 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



Activities 

The Activities help you practice real number concepts. You can select from two activities — 
Raining Reals and What Is My Property? Follow these steps to play the activity and complete 
your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press |ENTER| . 



Raining Reals 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IEMTER] to select it. 

2. As the numbers fall on your screen, quickly determine if the 
"raining" number is rational or irrational. 

3. Press |T| to move the number into the RATIONAL set, or press 
|T) to move the number into the IRRATIONAL set. If the 
answer is incorrect, the correct answer is displayed; press any 
key to resume play. 

4. Follow your teacher's instructions for how long to play the 
activity. 

5. What level did you play? 





| SELECT fln ACTIVITY 1 








"1 


Rflininc- REALS I 




3 


USE THE ARRDU KEYS 
TD SLIDE THE RUBBER 
Tn THE CnRRECT SET. 




SELE 


ICT i. PRESS [EATER] h 


& 



Scoring: Every correct 
placement earns 2 points. 

The game automatically 
ends if you have 
answered incorrectly four 
times (shown in the top 
right corner), or you press 
(QUIT) to stop. 



6. What was your final score? 



7. How many incorrect answers did you have? 

(Shown in top right corner of the screen.) 

8. Write a paragraph describing the activity. Describe your 
strategy for playing. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-24 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



Activities (continued) 



SELECT fln ACTIVITY 



HHflT IS MV PROPERTY? 



USE THE RRRDU KEYS 
TD PICK THE CDRRECT 
PRnPERTY. 



SELECT i. PRESS [ERTER] O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 16 
points. 



What Is My Property? 

1. Look at the equation and decide which single property, out of 
these six, it represents. 

• Commutative + 

• Commutative * 

• Associative + 

• Associative * 

• Distributive * Over + 

• Distributive * Over - 

2. Scroll through the property choices with and/or 0. To 
select a property, press [ENTER]. If the answer is incorrect, the 
correct answer is displayed; press any key to resume play. As 
you play the activity, record each equation and its property. 



3. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-25 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Investigate how the calculator deals with irrational numbers. 

In the Overview, you used the Pythagorean theorem to find the length of V~2~7 Draw a right 
triangle so that the hypotenuse has length V~2~7 Pythagoras (569-475 B.C.), a great Greek 
mathematician, discovered irrational numbers (numbers that are not rational and therefore are 
not ratios). There is a proof that, for example, V^cannot be written as a fraction. 



Hint: Draw each leg with length 1 inch. The hypotenuse is y'\ 2 +1 2 = \1 +1 = y 2 



Remember that V 2 x V 2 = 2. Picture this by envisioning a square whose sides measure V 2 units. 
You created this length in your picture above. 



Look at the square whose side has a length of y 2 on the Geoboard screen below. Can you see 
that the area is y^x V2~= 2 square units? Count it up! Shade in the area on the screen shown. 



+ 


+ + + + 


Area: 


+ 
+ 
+ 




2 


+ 


+ + + + 




DRflHlTFRHlFHflTlHEASlDPTn 



From the TI-73 Geoboard 
application 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-26 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Find the calculator decimal approximation for V~27 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Select the Float setting from the mode 
screen. 

Notes: See | Tip™ 2: Adjusting Your Calculator 
Settings for details. 

The TI-83 Plus mode screen varies slightly from the 
TI-73. 










|M0DE| 

until Float is 

highlighted 

lENTERl 




IMUytll 5c 


i En9 




atEEtTs 123456789 
agBffiff De9ree _ 


^31 Horiz r G-T V 








3. Return to the Home screen. 


[2nd] [QUIT] 




4. Calculate the decimal approximation 

for ^27 


[2HBi [v] 2 m 

lENTERl 










1.414213562 




5. Square your result. 

Note: Ans = previous answer. The calculator 
remembers that you entered VX2). 


m 










J"C2> 

1.414913569 




lENTERl 


Fins* 


2 



Is V 2 equal to the decimal 1.414213562? It looks like the calculator says this is true. Calculate 
1.414213562 2 to see. 



6. Calculate the square of 1.414213562. 



1 Q41 421 3562[H] 



lENTERl 



■K2) 






1.414213562 


Fins* 






2 


1.414213562^ 




1 . 999999999 



The answer shows 1.999999999, but you know you should get the answer 2. 

Be careful! When you use your calculator, you have to know your math. The calculator can do 
amazing math, but it only shows you an approximation for many answers. You have to 
understand the problem before you use the calculator. It is up to you to determine if calculator 
answers are reasonable and how you will use them. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-27 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Word Problem: Missy's Garden 

Missy wants to build a small fence around a garden in her backyard. The 
garden is in the shape of a right triangle. One leg is 2 meters and the 
other leg is 1 meter. The store sells fencing in tenths of a meter. 



2m 




1 m 



1. What is the exact perimeter of Missy's garden? Show all your work. 



Math Hint: Use the Pythagorean theorem to find the length of the third side of the garden, and then find the perimeter of the 
garden. (See the Real Numbers Overview on the calculator.) 

2. What length of fencing should Missy buy if the store only sells the fencing in tenths of a meter? 
Use the calculator. Show all your work. 



Calculator Hint: After you calculate the approximate answer on your calculator, try setting IMODEI so that Float=1. 

See i Tip™ 2: Adjusting Your Calculator Settings for details. This will give you one decimal place or tenths. Observe how the 

calculator displays the results! 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-28 



Chapter 1 : Number Sense 
Section 3: Real Numbers 



Name 
Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Word Problem: Jose and Maria's Backyard Pool 

Jose and Maria have a circular pool in their backyard. Their parents 
would like to make a cover for the pool. They bought a square piece of 
material whose sides are the same length as the diameter of the pool. 
The diameter of the pool is 3.5 meters. 




1. How much material will they have left over? Find the exact and approximate answers. Use the 
calculator. Show all your work. (See Hints below.) 



2. Exact answer: 



3. Approximate answer (to 3 decimal places): 

Calculator Hints: 

• Use Float = 3 on your calculator to display 3 decimal places. 

• Press [2nd] M to find the calculator's approximation for k. 
Math Hints: 

• Area of a square: A = s 2 , where s is the length of the sides of the square. 

• Area of a circle: A = n r 2 , where r is the radius of the circle (diameter = 2r). 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 1-29 



Chapter 1 : Number Sense Section 3: Real Numbers 




Number Sense: Real Numbers Teacher Notes 



Objectives 

• To illustrate the real number system in a Venn diagram. 

• To identify real numbers as rational numbers u irrational numbers. 

• To review writing rational numbers as terminating or repeating decimals. 

• To review writing irrational numbers as nonterminating, nonrepeating decimals. 



• To show physical representations of the irrational numbers, V 2 and n, and to review the 
Pythagorean theorem and the formula for finding the circumference of a circle. 

• To state the real number system properties — commutative, associative, and distributive — as 
well as the identity and inverse properties. 

Math Highlights 

This section starts with the building of the Venn diagram of the real number system. Definitions of 
rational and irrational numbers are given. Two examples of irrational numbers, V^and n, are 
developed. -{2~ is shown as the length of the hypotenuse of a right triangle with legs of 1 unit. % is 
shown as the circumference divided by the diameter for any circle. The statements of the properties 
of the real numbers follow. 

Common Student Errors 

• Many students may not have developed a solid understanding of number sets. Remind them 
that using rational and irrational numbers, they can name every location on a number line. 
Later in their studies of mathematics, this will be referred to as the Completeness Property of 
Real Numbers, which was an important discovery in mathematics. Later, they will also 
extend the real numbers to the complex numbers, a + h^[-\ - a + hi, which are numbers used, 
for example, in the study of the relationship between electricity and magnetism. 

• Students probably have used 22/7 or 3. 14 as an approximation of n. They may think that these 
values are exactly 71, but they are not equal to n. This provides an opportunity to talk about 
approximations to several decimal places in real problems. The worksheet problems give 
students an opportunity to find exact and approximate answers. There are wonderful web 
sites that show n to millions of places. Mathematicians are still searching for more place 
values. This study of n requires the use of computers to assist the search. 

• Some students may not be aware that the ratio of the circumference of a circle C divided by 
the diameter d is 71. C/d- n. This may be confusing because they have been told that 7t is 
irrational and is not a ratio. Yet n came from a ratio of circumference to diameter. It turns 
out that either C or d is also irrational. The mathematics to prove this is not given at this 
level; therefore, students have to accept this without much explanation. This is a deep 
discussion that will not be of interest to some students, but other students may find it 
fascinating. 



Topics In Algebra 1 ©2001 Texas Instruments Teacher Notes 1-30 



Chapter 1 : Number Sense 



Section 3: Real Numbers 



Student Worksheet Notes with Answers 




Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand number sense concepts relating to real numbers. Tell 
students how to find the Observations. 



WRITE THREE DIFFERENT 
IRRRTIDRRL RUBBERS. 



USE YDUR WORKSHEET. 



Students see this screen 
with three possible 
answers. 



Observation 1 

Write three different irrational numbers. Students show their 
work. 

Answers will vary. 



THREE EIIHMFLEL": 
27.i21i2iii2ilii2 . 

J? = £.fiHE7E131 ... 
i-JF = "1.23606797 . 



TRY THESE PROBLEMS . 
USE YDUR WORKSHEET. 



2E+2H : 
H*i02 : 
6*16 = 



Students should show 
that they know how to use 
the properties of the real 
number computations as 
shortcuts without the 
calculator. 



Students see the answers 
on the next screen. 



Observation 2 

Try these problems . . . 

Students use the real number properties to solve the problems, 

showing their work. 

• associative * property: 

25 * 24 = 25 * (4 * 6) = (25 * 4) * 6 = 100 * 6 = 600 

• distributive * over + property: 

8 * 102 = 8 * (100 +2) = (8 * 100) + (8 * 2) = 800 +16 = 816 

• distributive * over - property: 

6 * 46 = 6 * (50 - 4) = (6 * 50) - (6 * 4) = 300 - 24 = 276 



TRY THESE PROBLEMS . 
SDHE SOLUTIONS ARE: 



2E+2H = ££*<H*fi> = 6(1(1 
B*i02 = B*(iO0+£) = Bifi 
fi*Hfi = fifrCSO-'P = 276 



Topics In Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-31 



Chapter 1 : Number Sense 



Section 3: Real Numbers 



Activities 





| SELECT fln ACTIVITY | 








nr 


RAinina reals | 




3 


USE THE ARRDU KEYS 
TD SLIDE THE MJHBER 
Tn THE CnRRECT SET. 




SELECT i. PRESS [ENTER] O 



Scoring: Every correct 
placement earns 2 points. 
When students give an 
incorrect answer, the 
correct answer displays. 

The game automatically 
ends when they have 
answered incorrectly four 
times (shown in the top 
right corner), or they 
press (QUIT) to stop. 



■ M 


i 




B 


HHAT IS HY PROPERTY? 




USE THE ARRUU KEYS 
TO PICK THE CORRECT 
PROPERTY. 


SEL 


ECT £ PRESS [ERTER] O 



Scoring: Students get 
two attempts to answer. 
They earn 2 points for a 
correct answer, 1 point for 
a correct answer on the 
second try. 

They can earn up to 16 
points. 



Raining Reals 

Tell students to: 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. Determine if the "raining" number is rational or irrational. 

3. Press |TJ to move the number into the RATIONAL set, or press 
|TJ to move the number into the IRRATIONAL set. If the 
answer is incorrect, the correct answer is displayed; press any 
key to resume play. 

4. Follow your instructions. For example, students can play: 

• until they have answered incorrectly four times (no time limit) 

• until a certain amount of time has expired (high score wins) 

• until a certain score has been reached (first student to 
reach the score with the fewest misses wins) 

• over a period of time (days, weeks, etc.) for tracking 
improvement of high scores 

5. Record the level they played. 

6. Record their final scores. 

7. Record how many incorrect answers they had. 

(Shown in top right corner of the screen.) 

8. Write their strategy for playing the game. 

What Is My Property? 

Tell students to: 

1. Look at the equation and decide which one property, out of 
these six, it represents: 

• Commutative + 

• Commutative * 

• Associative + 

• Associative * 

• Distributive * Over + 

• Distributive * Over - 



2. Scroll through the choices with and/or and press IENTERI 
to select the correct property. If the answer is incorrect, the 
correct answer is displayed; press any key to resume play. As 
they play the activity, record each equation and its property. 

3. Record their scores. 



Topics In Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



1-32 



Chapter 1 : Number Sense Section 3: Real Numbers 

1 Try-It!™ on Your TI-73 or TI-83 Plus 

Tell students to: 

• Use the Pythagorean theorem to draw a triangle whose two legs = 1 unit and whose 
hypotenuse = V2~units. 



• Shade in the area on the Geoboard screen on the worksheets. 

• Go through the keystroke example to: 

Find the calculator decimal approximation for a/~2T 

Understand how the calculator approximates numbers. 

Understand that they must be conscientious about the mathematics involved. 

Word Problem: Missy's Garden 

Remind students to: 

• Use the Pythagorean theorem to find the third side of the garden and then the perimeter. 



• Set the decimal mode notation flMODEQ to Float and then to 1 (answer rounded to tenths), so 
they can see how the calculator displays answers. 



1. Exact perimeter: 1 + 2 + V 5 meters 

2. Length of fencing rounded to tenths: 5.2 meters 

Note: The number rounds down. This is mathematically correct, but impractical in the real world, where Missy would need to purchase 5.3 
meters in order to fence the garden. You may want to discuss meaningful interpretation of word problems with the students. 

Word Problem: Jose and Maria's Backyard Pool 

If necessary, review the formulas for area of a square and area of a circle. They are shown on the 
worksheet. 

Covering material left over: 

1. Exact: Area of square — area of circle - (3.5) 2 - ti(3.5/2) 2 = 12.25 - 3.0625 n square meters 

2. Approximate: 2.629 square meters (3 decimal places; use Float=3) 



Topics In Algebra 1 ©2001 Texas Instruments Teacher Notes 1-33 



Chapter 2: Linear Equations 
Section 1 : Using Graphs & Tables 



Name 
Date 



Linear Equations: Using Graphs & Tables 



Overview 



Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) (|TJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 



The Observations illustrate linear equation concepts relating to graphs and tables. Scroll through 
the Observations using (T| ([TJ to review, if necessary). Read each screen carefully. When you 
come to a Write an Observation screen, stop and write the answers to the questions on your 
worksheet. 



l!lft««IJ.HH«filiiim 
ui"im; li TABLE 



FIHD the snmTinn 

DF 
-x-fi = -3.£ 



USE YDUR WORKSHEET 



Observation 1 

Using a table, find the solution of _ x-6 = "3.5. 

First, find the solution by hand, making a table with at least five x 
and y values. You can start with any x value you want. Show your 
work. 



x 



y 



Next, graph your solution on a number line. Be sure to label all points 
on the number line. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-1 



Chapter 2: Linear Equations 
Section 1 : Using Graphs & Tables 



Name 
Date 



Activities 

The Activities help you practice graphs and tables. You can select from two activities — Beam 
Dale Up or Worksheet Activity. Follow these steps to play the activity and complete your 
worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press |ENTER| . 



5 



gaEJBHBH 



BEAH DHLE 



'bHpI 



FiriD THE SDLDTIDD 
TD GET DHLE BACK TD 
HIS SHIP. 



SELECT £ PRESS [ENTER] O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 



Beam Dale Up 

1. Look at the problem on the space ship and determine how to 
solve the equation for x from the four choices given. The 
values are ordered as they are on a number line. 

2. Press [TJ and |jj to move Dale the Martian over the correct x 
value, and then press [ENTER]. If the x value you pick is correct, 
Dale is beamed up to his ship! If the answer is incorrect on 
the second attempt, the correct answer is displayed; press any 
key to resume play. As you play the activity, solve each 
equation in the space below. Show all steps and work. 



3. What was your score? 





| SELECT HI! ACTIVITY | 


XI 




Mr 


PLEASE SEE YDUR 
WORKSHEET FDR 
HDRE ACTIVITIES. 








O 



Note: Press H or to 
leave this screen. 



Worksheet Activity 

1. Look at the table of values of equations Yi=2X+4.5 and Y2=7. 



2. 



X 


Ml 


Vz 





1.5 




.£ 


£.£ 




1 


fi.E 




i.E 


?.S 




2 


H.£ 




2.S 


9.5 




3 


iO.E 




V1B2X+4.5 



When is 2X+4.5=7 (or, when is Yi=Y2)? Look at the table 
carefully. The solution is between which two X values? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-2 



Chapter 2: Linear Equations 
Section 1 : Using Graphs & Tables 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Use the table feature on your calculator to search for the solution (when Yi=Y2). 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 



[2nd] [QUIT] 
(EXIT) [CLEAR] 



2. First, enter 2X+4.5 as Yi and 7 as Y2 in 
the Y= editor. 

Note: See § Tip™ 3: Graphing a Function in the 
Standard Window for more information. 

Note: On the TI-73, use H rather than |x,T,e,n| . 



[Y^I ICLEARl 

2 |X,T.0,/?| [+I4n5 

R lCLEARI 



Noti PlotE Plots 

WiH2X+4.5 

WzH7 

Wj = 

Wh = 

We = 

Ws = 



3. Change the table settings to those 
used in the Worksheet Activity. 



[2nd] [TBLSET] 


0.5 

R I ENTER | 
R I ENTER | 



TRBLE SETUP 

TblStart=0 

^Tbl=.5 
Indpnt: KH1E R^k 
Depend: |;B.B flsk 



4. Display the table. 



2nd] [TABLE] 



X 


Ml 


V2 





l.E 




.E 


E.E 




1 


fi.E 




l.E 


7.E 




2 


B.E 




2.E 


E.E 




3 


10. E 




ViB2X+4.5 



5. Change the table settings to focus on 
the range you found in the Worksheet 
Activity. Begin the table at the lower 
value and make the increments 
smaller. 



[2nd] [TBLSET] 

1 

0.1 



TRBLE SETUP 

TblStart=l 

^Tbl=.l 
Indpnt: KBOZ Rsk 
Depend: EBEE Rsk 



6. Display the table with the new 
settings. 



2nd] [TABLE] 



X 


V1 


V2 


1.1 

1.2 
1.3 
l.H 
l.E 
i.fi 


fi.E 
fi.7 
fi.E 
7.1 
7.3 
7.E 
7.7 




X=l 



7. The table still does not display the exact solution. What table settings would you choose in 
order to display the exact solution? 

TblStart= 

ATbl= 



8. What is the solution (when is Y1=Y2)? 

9. How do you know this is the solution? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-3 



Chapter 2: Linear Equations 
Section 1 : Using Graphs & Tables 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



Solution Search Using X-Y Graphs: Find the solution for the equation X+3=1 .7. First, use your 
number sense to estimate the solution for X+3=1 .7. Record your estimate here. 



Use the table feature on your calculator to search for the solution (when Yi=Y2). 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 



[2nd] [QUIT] 
(EXIT) [CLEAR] 



2. Set the window format as shown. 

Note: See | Tip™ 2: Adjusting Your Calculator 
Settings for more information. Screens are shown 
for the TI-83 Plus. There are slight differences on 
the TI-73. 



2nd] [FORMAT] 



Polar-GC 

Coor-dOff 

Gr-idOff Mafetilg 

RxesUTT 

LabelOn 

xprOff 




3. Enter both sides of the equation into 
the Y= editor as shown. 

Note: See i Tip™ 3: Graphing a Function in the 
Standard Window for more information. 

Note: On the TI-73, use {x\ rather than |x,T,e,n| . 



[Y^I ICLEARl 
1Q7 
F1 ICLEARI 
|XJ,9,/7| [+13 



Plod Plo(2 Plot? 

\ViB1.7 
WiBX+3 



4. Select ZDecimal to set the viewing 
window and automatically graph the 
functions. 



TI-83 Plus: 
[ZOOM] 4:ZDecimal 

TI-73: 

[ZOOM] 8:ZDecimal 



MEMORY 
ox 

2: Zoom In 
3: Zoom Out 
SBZDecinal 
DTZS^uare 



5. Trace Y1 =1.7. 

6. Trace Y2=X+3. 

Note: The function displays in the upper left corner 
of the screen; the X and Y values are displayed on 
the bottom of the screen. 



ITRACEI 

H or \V\ to trace a 

function 

and \z\ to move 

between functions 




1=1.7 



7. Find where X+3=1 .7. What is the solution? 

8. How do you know? 



9. Did you notice that the value of X+3 is 1 .7 when X= _ 1 .3? 



V1=i.7 ■ ■ / 








K="i.3 ■ ■ 


•1=1.7 ■ ■ 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-4 



Chapter 2: Linear Equations Name 

Section 1 : Using Graphs & Tables Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Solution Search: Write the solution and explain how you found the solution using graphs and 
tables for each of the problems below. 

For each problem: 

• Before you start, estimate the solution so you have an idea of where the solution is located. 

• Search for the solution of the equation on the calculator using graphs and table. 
Note: See i Tip™ 4: Creating a Table for additional help with the calculator. 

• Remember to change your viewing window or your table setting to do your search. 

Note: See f§ Tip™ 5: Adjusting the Viewing Window for additional help with the calculator. 

• Explain how you found the solution. 



Calculator Fact: The calculator only uses the variables X and Y for graphs and tables. If an equation uses letters other than X, you will 
have to enter the letter for the unknown variable as X in the calculator in order to make the graphs and tables for your solution search. 

1. p + 3 = l 



3x - 2 = 1.6 



1 5 7 
3. -x + - = - 

2 8 8 



4. 4 + 0.5C = 7 



Calculator Hint: Use ZStandard to change the graph window so that: -10<X<10 and -10<Y<10. 



Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 2-5 



Chapter 2: Linear Equations Section 1 : Using Graphs & Tables 



Linear Equations: Using Graphs & Tables Teacher Notes 




Objectives 

• To illustrate how to locate the real number solution of a linear equation using tables. 

• To illustrate how to locate the real number solution of a linear equation using a graphical 
method on a Cartesian (x-y) graph. 

Math Highlights 

In the table of values method, students see a table of values for the left and right side of the 
equation. They see that the x value, which makes the two sides of the equation equal, is the 
solution. They also see that they may need to refine the table of values to search for the solution. 

In the x-y graphical method, students graph both sides of the equation and find the intersection 
of the lines. If students have not graphed lines, they can first make a table of values and then plot 
the points to graph the lines. The x coordinate of the intersection of the lines is the solution. 

Common Student Errors 

• Using graphs and tables can mislead a student to think that they can always find the exact 
solution using these methods. Although they often will find exact solutions using these 
methods, using algebra will give exact answers for these equations. Have students try to 
search for the solution to x + a/~2 _ = a/~7T The exact answer is x = ^fl~- a/~2 _ = 1.2315377 . . . 

• At times, introducing the algebraic solution of equations gives students just the mechanics of 
doing a problem. Algebraic methods alone usually do not invite the student to reason out the 
solution using number sense. The graphs and tables method gives students the opportunity to 
see the values of each side of the equation so they can see when the right side and left side of 
the equation are equal. 

Visual learners benefit by seeing the numbers and graphs first, and then by using these as the 
tool to find the solution. 

• Some students are able to see the solution to an equation using their number sense and may 
have difficulty taking the time to show their work. This may also be an issue in 

Chapter 2: Linear Equations, Section 2: Using Algebra. Encourage the use of written 
mathematics and drawing graphs and tables as a communication tool. Have students look in 
newspapers for graphs and tables of information to show real examples for the need for this 
communication skill. 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 2-6 



Chapter 2: Linear Equations 



Section 1 : Using Graphs & Tables 



Student Worksheet Notes with Answers 




Overview 

Tell students: 

1. How to find the Overview or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand linear equation concepts relating to graphs and 
tables. 

If necessary, tell students how to find the Observations section for this section. 





| HRITE fln DBSERYHTinn ... | 


USinG A TABLE 




FIRD the snmTinn 

DF 
-x-fi = -3.£ 




USE 


YDUR WORKSHEET 


O 



Observation 1 

Using a table, find the solution of _ x-6 = "3.5. 

First, find the solution by hand, making a table with at least five x and 
y values. The students can start with any x value they want. Students 
show their work. 



Students see the table 
and graph screens as 
they finish viewing the 
observation. 



Next, they graph the solution on a number line. Remind them to label 
all points on the number line. 

Students make a table by hand on the worksheet to search for the 
solution of~x - 6 - -3.5. Then they transfer these x and y values to 
a number line. Look for correct labeling. 



■is 



M'M'IgHM 



x-fi 



■2.£ 
■3 



"3.£ 



-3.£ 



"3.£ 



x~Z£ 



-x-fi = -3.£ 



< l * I 



VDU CAR 
GRAPH THE 

jnLUTinn . 



■++ 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



2-7 



Chapter 2: Linear Equations 



Section 1 : Using Graphs & Tables 



Activities 



5 



gaEJBHBH 



BEAH DHLE 



'bHpI 



FinD the sdldtidd 

TD GET DHLE BACK TD 
HIS SHIP. 



SELECT £ PRESS [EDTER] O 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

Students can earn up to 
10 points. 



Beam Dale Up 

Tell students to: 

1. Look at the problem on the space ship and determine how to 
solve the equation for x from the four choices given. The 
values are ordered as they are on a number line. 

2. Press [TJ and |jj to move Dale the Martian over the correct x 
value, and then press [ENTER]. If the x value they pick is 
correct, Dale is beamed up to his ship! As they play the 
activity, students record the solution to each equation, 
showing all steps and work. If the answer is incorrect on the 
second attempt, the correct answer is displayed; press any 
key to resume play. 

3. Record their scores. 





| SELECT An ACTIVITY | 


X! 




Mr 


PLEASE SEE YDDR 
WORKSHEET FDR 
HDRE ACTIVITIES. 








O 



Note: Press [T] or to 
leave this screen. 



Worksheet Activity 

Tell students to: 

1. Look at the table of values of the expressions, Yi=2X+4.5 and 
Y2=7. 

2. Answer the questions: When is 2X+4.5=7 (or, when is Y1=Y2)? 
The solution is between which two X values? 

The solution for 2X+4.5=7 is found between 1 and 1.5. 

Students will continue to search for the solution in the (J) Try-It! 
section. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



2-8 



Chapter 2: Linear Equations 



Section 1 : Using Graphs & Tables 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Tell students to: 

• Follow the steps exactly on the calculator, using the table feature to find the solution. 
Example screen pictures are displayed on the worksheet for students to compare with the 
calculator screen. This keystroke exercise lets students define Yi =2X+4.5 and Y2=7. 

• Determine what the table settings should be for an exact solution and record them on their 
worksheet. 

Answer: ATbl=0.25 and TblStart=1 . 



TABLE SETUP 

TblStart=l 

^Tbl=.25 
Indpnt: \3BJE fisk 
Depend: [ilffg Rsk 



X 


Vi 


Vz 


nR^B 


fi.E 
? 




is 


?S 




i.7£ 


B 




2 


BS 




£.££ 


9 




2.£ 


9.£ 




X=1.25 



• Find the solution and record it. Answer: Yi =Y2 when X=1 .25. 



Solution Search Using X-Y Graphs: Find the solution for the equation X+3=1 .7. 

Tell students to: 

• Estimate the solution and record it on their worksheets. 

• Follow the steps exactly on the calculator. Example screen pictures are displayed on the 
worksheet for students to compare with the calculator screen. This keystroke exercise lets 
students find the solution where X+3=1 .7. 

• Record the solution and explain their answers on the worksheet after step 6. 

Answers will vary. Student estimates using number sense should be close to the answer 
_ 1 .3. They see that the two lines intersect at x= _ 1 .3. 

Note: See the TI-83 Plus Guidebook, for information on the TI-83 Plus automatic feature "Intersection," which is not covered in this 
section. This feature is not on the TI-73. 

Solution Search: Students write the solution and explain how they found the solution using 
graphs and tables for each of the problems below. 

Tell students to: 

• Review how to use the graphing features of the calculator to search for a solution. 

• Find the intersection of the lines by tracing the graph. Remind students that the viewing 
window must be set appropriately to find the intersection, and finding the exact solution is 
not guaranteed; they must combine the two methods to find the solutions. 



Use number sense to complete the search. 

p + 3 = 1 when p = - 2 



2. 3x - 2 = 1.6 when x = 1.2 



3. 



1 5 7 
-x + - = - 

2 8 8 



1 

when x = — 

2 



4. 4 + 0.5C = 7 when C = 6 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



2-9 



Chapter 2: Linear Equations 
Section 2: Using Algebra 



Name 
Date 



Linear Equations: Using Algebra 



Overview 




Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 



The Observations illustrate linear equation concepts relating to algebra. Scroll through the 
Observations using (7J ([JJ to review, if necessary). Read each screen carefully. When you come 
to a Write an Observation screen, stop and write the answers to the questions on your worksheet. 



HRITE fln DBSERYRTIDn . 



x-£ = B SOLVE FDR :■:: 



USE YDUR UDRKSHEET 



Observation 1 
x-5 = 8 



Solve for x. Show all of your work below. 



2 x = g L'DL'.'E FDR ■: 



USE YDDR UDRKSHEET 



Observation 2 



Solve for x. Show all of your work below. 



HRITE Rn DBSERYRTIDn . 



H-x = 10 SOLVE FDR :■:: 



USE YDUR UDRKSHEET 



Observation 3 
4-x = 10 



Solve for x. Show all of your work below. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-10 



Chapter 2: Linear Equations 
Section 2: Using Algebra 



Name 
Date 



Activities 

The Activities help you practice algebraic concepts. You can select from three activities — 
Solve It!, Beam Dale Up, and Free Fall. Follow these steps to play an activity and complete your 
worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press |ENTER| . 



HH 








Qt" 


JDL'.'E IT !| 




PICK THE CORRECT 
STEPS Tn SOLVE 
THE EOUflTinn. 




SELE 


:CT i. PRESS [ERTER 


] O 



Scoring: You get two 
attempts to pick the 
correct step or steps. You 
get 2 points for a correct 
choice on the first try, and 
1 point for a correct 
choice on the second try. 
You get an additional 2 
points for the correct 
solution. 

The total number of points 
available varies. 



Solve It! 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IEMTER] to select it. 

2. Look at the algebraic expression at the top of the screen and 
decide what step to take to solve the equation for x. 

3. Press or to cycle through steps to choose from, and then 
press |ENTER| to select the correct step (some problems require 
two steps). If your second choice is incorrect, the correct step 
is displayed; press any key to continue play. As you play the 
activity, write the equations, the steps required to solve them, 
and the solutions to the equations. 



4. What level did you play? 

5. What was your score? 



out of 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-11 



Chapter 2: Linear Equations 
Section 2: Using Algebra 



Name 
Date 



Activities (continued) 





| SELECT An ACTIVITY | 


X! 




— r 


REAH DALE H Up| 




FID.D THE SDLUTIDR 
TD GET DALE RACK TD 
HIS SHIR. 




SELECT i. PRESS [ENTER] 


O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 



Beam Dale Up 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. Look at the problem on the space ship and determine how to 
solve the equation for x from the four choices given. 

3. Press |TJ and \T\ to move Dale the Martian over the correct x 
value, and then press IENTERI . If the x value you pick is correct, 
Dale is beamed up to his ship! If the answer is incorrect on 
the second attempt, the correct answer is displayed; press any 
key to resume play. As you play the activity, solve each 
equation in the space below. Show all steps and work. 



4. What level did you play? 

5. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-12 



Chapter 2: Linear Equations 
Section 2: Using Algebra 



Name 
Date 



Activities (continued) 





| SELECT An ACTIVITY | 


41 




ir 


FREE FALL I 




HHAT CUES UP.. 
MUST CUHE DUUR 




SELECT i. PRESS [ERTER] O 



Scoring: Points are 
based on how quickly you 
solve each equation. 

The game automatically 
ends if four missed 
equations stack up, or 
you press (QUIT) to stop. 



Free Fall 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. When you are ready to start, press any key. 

3. Watch the equation as it falls, and quickly solve for x. Enter 
the solution (press O for negative numbers), and press IENTERI 
before the equation hits bottom. If you give an incorrect 
answer, the correct answer is displayed; press any key to 
resume play. The incorrect equation stacks up at the bottom 
of the screen, giving you less time to solve the next equation. 

4. Follow your teacher's instructions for how long to play the 
activity. 



5. What level did you play? 

6. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-13 



Chapter 2: Linear Equations 
Section 2: Using Algebra 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Can your calculator check your work? Is X=2 the solution to the equation X+3.1 =5.5? 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 

From the Home screen, the calculator 
can tell you if a sentence is TRUE or 
FALSE (1=TRUE and 0=FALSE). 


[2nd] [QUIT] 




(EXIT) | CLEAR | 


2. First, check for the value currently 
stored in X. 

Note: On the TI-73, use pel rather than |x,T,e,n|. 










|X,T,G,n| 




X 

-3.2 




I ENTER | 


3. What is the value of X stored in your calculator? 

Check around the class. Most likely, there are many different values stored to X. 


4. Next, find out: Is X+3.1 =5.5 true or 
false when X=2? When you tell the 
calculator that X=2, this is called 
storing a value in X. 

Note: On the TI-73, use pel rather than |x,T,e,n|. 










2|STO||X,T,G,n| 




2*X 




| ENTER | 




5. Enter the expression X+3.1 =5.5. This 
takes three steps. 

a. Enter the first part of the 
expression: X+3.1 . 

Note: On the TI-73, use pel rather than |x,T,e,n|. 










|X,T,e,n|l±J 3LJ 1 




2*X 

2 
X+3.1 




b. Enter the equal sign (=) for 
the test. 


[2nd] [CATALOG] until = 
is highlighted 

I ENTER | 










CRTRLOG 
► = 

< 
> 




c. Now, complete the sentence 
and see the result. Since the 
result is 0(1=TRUE and 
0=FALSE), the sentence 
X+3.1 =5.5 is false when X=2. 


5Q5 
I ENTER | 










2*X 

2 
X+3. 1=5.5 







6. Test another point. Try X=3. Is the sentence true or false? What value do you think makes the 
sentence true? 

Hint: You do not have to type in the expressions again. 

• On the TI-73, press to highlight previous entries, and press |enter| to paste an entry on the current line. You can edit 
the line and use it again. 

• On the TI-83 Plus: [2nd] [entry] displays previous entries. When you get to the one you want, you can edit the line and 
use it again. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 2-14 



Chapter 2: Linear Equations Name 

Section 2: Using Algebra Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Additional Problems — Solve the following equations by hand. Show all of your work. Then test 
your solution using the calculator as shown in the |j) Try-It! example on the previous page. 

1. x - (-4) = 12 



3 1 5 
2. -W - - = - - 

4 4 8 



5.25 + P = -3.5 



Hint: To find = and other relations: 

• TI-83 Plus: Press [2nd] [test], and then select the relation you want. 

• TI-73: Press [2nd] [text] to enter the text editor, select the relation you want, press [enter], select Done, and press [enter]. 



Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 2-15 



Chapter 2: Linear Equations Section 2: Using Algebra 



Linear Equations: Using Algebra Teacher Notes 

Objectives 

• To review one-step and two-step linear equations. 

• To review the idea of isolating the variable, balancing equations and checking solutions. 

• To review the properties of equality. 

Math Highlights 

This section opens with an explanation of the idea of balancing equations using a pan balance. 
The properties of equality are displayed. Then, examples of solving linear equations of the forms 
x + a = b, ax = b, and ax + b = c are shown. These examples start with word problems and are 
then modeled with linear equations, solved, and the solution is checked. 

Common Student Errors 

• Students may have a hard time deciding which steps to follow to solve an equation. In 
particular, if they are given an equation in the form x + a = b, they may choose the wrong step 
to take if the equation is given as a + x = b. Students might make sign errors as they add or 
subtract from both sides of the equation. 

• Students should connect the idea of a zero model from working with integers; for example, 
they should connect 7 + _ 7 = with the concept of an additive inverse. They use the additive 
inverse to create the zero model. The term zero model is not discussed. 

• Students should notice that they are using the multiplicative inverse to isolate the variable 
when they multiply or divide both sides of equations. 

• Although this section deals with the mechanical way of finding the solution set, students 
should be reminded that they should check to see if the solution is reasonable. They need to 
keep using number sense. 

• Many students are able to see the answer using number sense without the written work. 
Learning how to write mathematics correctly is part of the communication skill and needs to 
be encouraged. This can cause frustration for students who find the problems easy to solve 
"in their heads." 

Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 2-16 




Chapter 2: Linear Equations 



Section 2: Using Algebra 



Observations 

The Observations help students understand algebraic concepts relating to linear equations. If 
necessary, tell students how to find the Observations. 



■!l*H*lil.|*H;VMH.IilHI 


Oh<;f>rvatinn 1 


X-E = B SOLVE FDR x: 
USE YDUR WORKSHEET 

O 




x-5 = 8 




HJ^.III.I^I^^H 


X-E = B SOLVE FDR X 








IWRJ 171 




Students solve for x. The 
answer is displayed on 
this screen. 


x-E+E = H+E MiHlENh* 
x = 13 

BTJSa 13-5 = B -/ 


O 






Observation 2 


l!l*U*lil.|:U*linU.h1H 
2 v = q SDLVE FDR x: 

USE YOUR WORKSHEET 

O 








■ DID YDU DESERVE ... ■ 






3 .. _ _ SDLVE FDR X 




Students solve for x. The 
answer is displayed on 
this screen. 


|*| x = |*s| 


NDLTIPLY 
EDTH SIDE 

»4 1 


B 




x = fi | 








W.\l\M 


* 












| HRITE RR DBSERVRTIDR ... | 


Observation 3 


H-x = 10 SULVE FUR x: 
USE YOUR WORKSHEET 

O 




4-x = 10 






| DID YDU DESERVE ... | 


H-x = ID SDLVE FDR x: 








iySHK 








! 




Students solve for x. The 


■x = fi \\ 


"!bna* 




answer is displayed on 
these screens. 




O 



Solve for x. Students show all their work. 



Solve for x. Students show all their work. 



Solve for x. Students show all their work. 



■.ui'j.m.im.im 

H-x = 10 SDLVE FDR x: 



H-H-x = 10-H 

~JL = ±. 
-1 -1 

x = "fi 



ram 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



2-17 



Chapter 2: Linear Equations 



Section 2: Using Algebra 



Activities 



SELECT RR ACTIVITY 



5DLUEIT! 



PICK THE CORRECT 
STEPS Tn SOLVE 
THE EQUHTinn. 



SELECT £ PRESS [ERTER] O 



Scoring: Students get 
two attempts to pick the 
correct step or steps. 
They get 2 points for a 
correct choice on the first 
try, and 1 point for a 
correct choice on the 
second try. They get an 
additional 2 points for the 
correct solution. 

The total number of points 
available varies. 



Solve It! 

Tell students to: 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. Look at the algebraic expression at the top of the screen and 
decide what must be done to solve the equation for x. 
Students must select from the choices offered; this activity 
presents only one sequence of steps (to first isolate x and then 
change the coefficient of x to 1), although other sequences 
may be correct. 

3. Press or to cycle through steps to choose from, and then 
press IENTERI to select the correct step (some problems require 
two steps). If the second choice is incorrect, the correct step 
is displayed. They must press a key to continue play. As they 
play the activity, students should write the equations, the 
steps required to solve them, and the solutions. 

4. Record the level they played. 

5. Record their scores. 



SELECT RR ACTIVITY 



BERH DRLE 



bHpI 



FIRD THE SDLUTIDR 
TD GET DRLE BACK TD 
HIS SHIP. 



SELECT i. PRESS [ERTER] 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

Students can earn up to 
10 points. 



Beam Dale Up 

Tell students to: 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. Look at the problem on the space ship and determine how to 
solve the equation for x from the four choices given. 

3. Press |T| and [►] to move Dale the Martian over the correct x 
value, and then press IENTERI . If the x value they pick is 
correct, Dale is beamed up to his ship! As they play the 
activity, students record the solution to each equation, 
showing all steps and work. If the answer is incorrect on the 
second attempt, the correct answer is displayed; press any 
key to resume play. 

4. Record the level they played. 

5. Record their scores. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



2-18 



Chapter 2: Linear Equations 



Section 2: Using Algebra 



Activities (continued) 





| SELECT An ACTIVITY | 


41 




ir 


FREE FALL I 




HHAT CUES UP.. 
MUST CUHE DUUR 




SELECT i. PRESS [ERTER] O 



Scoring: Points are 
based on how quickly 
students solve each 
equation. 

Unless you specify point 
or time limits for this 
activity, students can play 
the activity when four 
missed equations stack 
up, or they press (QUIT) 
to stop. There is no time 
limit. 



Free Fall 

Tell students to: 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. When they are ready to start, press any key. 

3. Watch the equation as it falls, and quickly solve for x. Enter 
the solution (press O for negative numbers), and press IENTERI 
before the equation hits bottom. If students give an incorrect 
answer, the correct answer is displayed; press any key to 
resume play. The incorrect equation stacks up at the bottom 
of the screen, giving them less time to solve the next equation. 

4. Follow your instructions. For example, students can play: 

• Until they have answered incorrectly four times (no time 
limit). 

• Until a certain amount of time has expired (highest score 
with the fewest misses wins). 

• Until a certain score has been reached (first student to 
reach the score with the fewest misses wins). 

• Repeatedly over a period of time (days, weeks, etc.) for 
tracking improvement of high scores. 

5. Record the level they played. 

6. Record their scores. 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Tell students to: 

• Solve the following equations by hand and show all of their work. 

• Test their solutions using the calculator as shown in the (J) Try-It! example on the previous 
page. 



1. x - (-4) = 12 



when 



x = . 



3 1 5 
2. — w - — = - — 

4 4 8 



when 



w = - — 

2 



3. 



5.25 + P = -3.5 



when 



-8.75 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



2-19 



Chapter 3: Linear Functions 
Section 1 : Slope with Grid 



Name 
Date 



Linear Functions: Slope with Grid 



Overview 




Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate the slope of a straight line. Scroll through the Observations using \±\ 
(|T) to review, if necessary). Read each screen carefully. When you come to a Write an 
Observation screen, stop and write the answers to the questions on your worksheet. 

Observation 1 



What do you notice about the slope of straight lines? Write your 
thoughts. 





| HRITE fln DBSERYHTinn ... | 


HBDUT THE SLOPE DF 
STRAIGHT LITlES. 


■ ■ -v^i-^ 7 ^- 
































::::<> 







Activities 

The Activities help you practice determining the slope of a line using a grid. You can select from 
two activities — Screen Cross or Linked Calculators Screen Cross. Follow these steps to play the 
activity and complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press jEMTERj . 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-1 



Chapter 3: Linear Functions 
Section 1 : Slope with Grid 



Name 
Date 



Activities (continued) 



SELECT AA ACTIVITY 



f 



1. SCREED CRDSs] 



FiriD THE SLDPE 
BETHEER THE GI'.'ETl 
ERDPniRTS. 



SELECT £ PRESS [ERTER] O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 



Screen Cross 

1. Read the directions on the screen, and then press any key to 
continue. 

Note: Repeat steps 2 and 3 for line segments 2 through 5. 

2. Calculate the slope between the two points. Record your 
work below. 

3. Press or to view the choices for the slope (UNDEF = 
undefined slope). When you think the correct slope is 
displayed, press IENTERI . 



segment 1: 
segment 2: 
segment 3: 
segment 4: 
segment 5: 



4. What was your score? 





| SELECT AA ACTIVITY | 


£*| 


LinnED 

CALCULATORS 




L=i=jr 


2. SCREER CRDSS 








FIRD THE SLOPE 
P-ETHEEn THE GIVER 
ERDPDiriTS. 




SELEC 


T £ PRESS [ERTER] ^ 


& 



Scoring: There are no 
points awarded in the 
linked version. You must 
answer correctly before 
the next line segment is 
shown. 

The player who reaches 
the right side of the grid 
first wins. 



Linked Calculators Screen Cross 

Play Screen Cross against another student. Race another student 
across the screen by calculating the slopes more quickly than 
your opponent. 

1. Connect two similar calculators using a unit-to-unit cable. 

2. Use the grid to help determine the slope of the line segment as 
quickly as possible. 

3. Select the slope as you did in Screen Cross. 

4. Who won? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-2 



Chapter 3: Linear Functions 
Section 1 : Slope with Grid 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Draw a line segment with endpoints at ("2,2) and (3,~2). Use the Line( command, which draws 
line segments on the graph screen. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 



[2nd] [QUIT] 
(EXIT) [CLEAR] 



2. Check to see if any functions or 
statistical plots are turned on. 



PlotZ Plots 

WiH2X+l 
Wz=-2X-1 

Wh = 



3. Turn off statistical plots or functions, 
if necessary. 

Note: See | Tip™ 8: Creating a Statistical Plot for 
more information. 



E,E,H,orE] 

IENTERI to deselect 



Ploti 


Pl*t£ 


Plots 


Wi=2X+l 




Wz = 


-2X-1 




W;= 






Wh = 






We = 






Ws = 






W? = 







4. Display the window format screen. 



2nd] [FORMAT] 




PolarGC 
CoordOff 
GridOn 

FlxesOff 
Label On 
xprOff 



5. Select GridOn. 



TI-83 Plus: 

RIFim fENTER] 

TI-73: 

Fim fENTER] 



PolarGC 

CoordOff 

GridOff H3EIIS 

flxesOff 

Label On 

xprOff 




6. Display the ZOOM menu. These 
settings set the viewing window 
automatically. 

Note: For more information, see § Tip 5: Adjusting 
the Viewing Window. 



[ZOOM] 



7. Select ZDecimal. 

Note: This also displays the graph screen 
automatically. 



TI-83 Plus: 
4:ZDecimal 

TI-73: 
8:ZDecimal 



MEMORY 
ox 
Zoom In 
Zoom Out 
ZDecimal 
ZS^iuare 
6:ZStandard 
7-i-ZTrig 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-3 



Chapter 3: Linear Functions 
Section 1 : Slope with Grid 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



To Do This 



Press 



Display (TI-83 Plus shown) 



8. Select the DRAW menu. 



TI-83 Plus: 
[2nd] [DRAW] 



TI-73: 

[DRAW] 



9. Select the Line( command, which 
draws line segments on the graph 
screen. 



2:Line( 



juaaa points sto 

TTcIrDraw 


fflLineC 

3: Horizontal 


4:Uertioal 


5:Tan9entX 


6:DrawF 


7-i-ShadeC 



10. Move the cursor to ("2,2). 

11. Set the endpoint (-2,2). 



[HE, EL or H 



ENTER 



■ 




K=-E . . 


V=£ . . . 



12. Move the cursor to (3,-2). 

13. Set the other endpoint (3,-2). The line 
segment is drawn. 



E,E,H,orE] 



ENTER 



14. Clear your drawing with ClrDraw, if 
desired. 



TI-83 Plus: 

[2nd! [DRAW] 1 :ClrDraw 



TI-73: 

[DRAW] 1 :ClrDraw 



. POINTS STO 

[rDraw 
_ LineC 
3: Horizontal 
4:Uertioal 
5:Tan9entt 
6:DrawF 
7-i-ShadeC 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-4 



Chapter 3: Linear Functions 
Section 1 : Slope with Grid 



Name 
Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Draw the Slopes! 

1. On your calculator use Line to draw segments that have the following slopes (m), and then 
copy the graph onto the screens below. 



a. m = 1/2 



b. m = 2/4 











c. m = 3/2 



















d. m = -2/3 











2. Compare your graphs with others in your class. Do you all get the same graph? If not, why? 



3. Compare the four segments drawn. Record your observations. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-5 



Chapter 3: Linear Functions 



Section 1 : Slope with Grid 



Linear Functions: Slope with Grid 




Teacher Notes 



Objectives 

• To impose a grid on a line to quantify the steepness of a line. 

• To introduce slope as the ratio of the vertical change divided by the horizontal change. 

• To illustrate the slope characteristics of lines as positive, zero, negative, or undefined (no 
slope). 

• To associate the terms with the appropriate graph of a line: increasing, horizontal, 
decreasing, or vertical. 

• To observe that the slope of a straight line is a constant. 

Math Highlights 

This section defines slope as the steepness of a line. It begins with a bike riding along a 
piecewise linear path. Students see the definition of slope as a ratio: 

vertical change 



Slope = m- 



nse 



horizontal change run 



A grid is imposed on the bike path to help illustrate how students can quantify the slope of each 
line segment. Next, lines with positive, zero, negative, and no slope are illustrated. 

Common Student Errors 

• Students may have difficulties counting the spaces between grid points; therefore, they may 
count the grid points instead of the spaces. For example, students who count grid points may 
think that the slope shown on the screen below is 7/4 instead of 6/3. Using a Geoboard or 
grid paper, redraw the line segment to help these students count the distance between the 
grid points rather than the points themselves. 




• In the screen below, the rise/run of the fourth segment is calculated as -6/5. For some 
students, associating "down 6 units, or _ 6" with the word rise can be confusing. The use of 
the terms vertical change or horizontal change helps students understand that change could 
be up or down, right or left. 



^KB 




RISE _"fi __fi 


/. . ..\ 


/. . . . i\ 


/....: .\ 


/.....:. X 


/ 


■ (eoni^j ■ ■ ■ \" ■ ■ ■ 


■■■■■/■ 







Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-6 



Chapter 3: Linear Functions 



Section 1 : Slope with Grid 



Common Student Errors (continued) 

• Students can calculate the slope for the fourth segment in four ways. 

With the animation to show direction, students usually will begin counting with the upper 
left-hand point on the segment. 



1E3MEB 



RISE _-fi . 
RIM "+£' 




or 



5 spaces to the right (+5) and 

6 spaces down ( _ 6) 

to get -6/5 



^KB 




RISE _-fi __fi 

Run '+£- £ 


/ . _:\ 


::::::/: Tl^ :::: 


/.....:. X 


/ 


■ (-:*ni5: ►■ V ' ' ' 


■■■■■/■ 







6 spaces down ( _ 6) and 

5 spaces to the right (+5) 

to get -6/5 



Without the animation to show direction, students may be as likely to begin counting from 
the lower right-hand point on the segment. 




or 



6 spaces up (+6) and 

5 points to the left ( _ 5) 

to get 6/-5 





| FDR Rnv LinE | 




RISE _"fi __fi 

rim ~+e~ e 


A . . . \ 


: : : :/ : A IN, : : : : 


/.....:. X 


/ 


: t &z9\.:^.:s ■ ■ ■ 


■■■■■/■ 









5 points to the left ( _ 5) and 

6 spaces up (+6) 

to get 6/-5 



Slope = m- 



6 -6 



_6 

5 



•■ 



All four ways of counting are correct, resulting in the same slope. The Observations reinforce 
this, stating, "The slope between any two points on a line is always the same ratio." 



Student Worksheet Notes with Answers 




Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out the new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-7 



Chapter 3: Linear Functions 



Section 1 : Slope with Grid 



Observations 

The Observations help students understand the slope of a straight line. 
If necessary, tell students how to find the Observations for this section. 

Observation 1 

Students write what they observe about the slope of straight lines. 

Answers may vary. Students observe that a line has constant slope. 



i!i*u*iii.i*u:iinu.iim 


HBDUT THE SLOPE DF 
STRAIGHT LITlES. 


































■ ■■■o 





Activities 



SELECT AA ACTIVITY 



f 



1. SCREED CRDSSI 



FiriD THE SLDPE 
P-ETHEEA THE GIVER 
EADPniATS. 



SELECT £ PRESS [EATER] O 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

Students can earn up to 
10 points. 



Screen Cross 

Tell students to: 

1. Read the directions on the screen, and then press any key to 
continue. 

Note: Repeat steps 2 and 3 for line segments 2 through 5. 

2. Calculate the slope between the two endpoints. Record their 
work. 

3. Press or to view the choices for the slope (UNDEF = 
undefined slope). When they think the correct slope is 
displayed, press IENTERI . 

4. Record the endpoints and slopes for each segment and their 
final score. The segments are different on each calculator and 
each time the game is played. 



H41ttf:liY:T4il'm'a 


L=i=jr 


LIRKED 
CALCULATORS 




2. SCREER CRDSS 






FIRD THE SLDPE 
P-ETHEEA THE GIVER 
ERDPDIRTS. 




SELEC 


T £ PRESS [EATER] ^ 


& 



Scoring: There are no 
points awarded in the 
linked version. Students 
must answer correctly 
before the next line 
segment is shown. 

The player who reaches 
the right side of the grid 
first wins. 



Linked Calculators Screen Cross 

Tell students to: 

1. Connect two similar calculators using a unit-to-unit cable. 

2. Use the grid to help determine as quickly as possible the slope 
of the line segment. 

3. Select the slope as they did in Screen Cross. 

4. Record which player won. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-8 



Chapter 3: Linear Functions 



Section 1 : Slope with Grid 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Students follow the example, which covers drawing a line on the graph screen from specified 
endpoints using the Draw menu. 

Draw the Slopes! 

1. These are sample answers only. Segment location varies depending on the starting point 
used. 



a. and b. 



c. and d 



n= I 



-I 



-I 



*4 



-! 



2. Students should notice that their segments are not necessarily the same as others depending 
on the starting point used. Later, they will see that the slope and a point determine a line. 

3. Students should notice that 1/2 and 2/4 have the same steepness. These segments are parallel 
(or on the same line). They should also observe that segments with slopes, "2/3 and 3/2, are 
perpendicular line segments. See graphs above. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-9 



Chapter 3: Linear Functions 
Section 2: Slope Using Coordinates 



Name 
Date 



Linear Functions: Slope Using Coordinates 



Overview 



Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate mathematical concepts relating to finding the slope using graph 
coordinates. Scroll through the Observations using |T) (|T) to review, if necessary). Read each 
screen carefully. When you come to a Write an Observation screen, stop and write the answers to 
the questions on your worksheet. 



WRITE lin DESERVflTinn . 



If liriY SET DF THREE 
FDiriTJ CDLLiriEfiF; I' 



URITE THEliriJMEF; 
DR VIIUR WORKSHEET. 



Is every set of three coordinate points collinear? Write your 
thoughts below. 



HRITE Rn IlBSERYRTinn . 



FiriD THE SLDRE DF THE 

LinE THRnuuH i:i..;:i *. i:-h..b:i 
HHICH is cdrrect ? 

-^ 



OR.. 



2-(-11 



Which is the correct way to calculate the given slope? Write your 
thoughts below. 



Activities 

The Activities section helps you practice finding a slope using graph coordinates. You can select 
from two activities — Screen Cross or Linked Calculators Screen Cross. Follow these steps to 
play the activity and complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press jEMTERj . 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-10 



Chapter 3: Linear Functions 
Section 2: Slope Using Coordinates 



Name 
Date 



Activities (continued) 



SELECT AA ACTIVITY 



f 



1. SCREED CRDSs] 



FiriD THE SLDPE 
BETHEER THE GI'.'ETl 
ERDPniRTS. 



SELECT £ PRESS [ERTER] O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 



Screen Cross 

This activity is similar to the Screen Cross in the Slope with Grid 
section. There is no grid displayed, but the endpoints are given. 

1. Read the directions on the screen, and then press any key to 
continue. 

Note: Repeat steps 2 and 3 for line segments 2 through 5. 

2. Calculate the slope between the two points. Record your 
work below. 

3. Press or to view the choices for the slope (UNDEF = 
undefined slope). When you think the correct slope is 
displayed, press IENTERI . 



point 1 (x u y0 point 2 (x 2 ,y 2 ) 



slope 



segment #1 
segment #2 
segment #3 
segment #4 
segment #5 



4. What was your score? 





| SELECT AA ACTIVITY I 


£*| 


LinnED 

CALCULATORS 




L=i=jr 


2. SCREER CRDSS 








FIRD THE SLOPE 
P-ETHEEn THE GIVER 
ERDPDiriTS. 




SELEC 


T £ PRESS [ERTER] ^ 


& 



Scoring: There are no 
points awarded in the 
linked version. You must 
answer correctly before 
the next line segment is 
shown. 

The player who reaches 
the right side of the grid 
first wins. 



Linked Calculators Screen Cross 

Play Screen Cross against another student. Race another student 
across the screen by calculating the slopes more quickly than 
your opponent. 

1. Connect two similar calculators using a unit-to-unit cable. 

2. Use the grid to help determine as quickly as possible the slope 
of the line segment. 

3. Select the slope as you did in Screen Cross. 

4. The player who reaches the right side of the grid first wins. 

5. Who won? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-11 



Chapter 3: Linear Functions 
Section 2: Slope Using Coordinates 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Use the calculator to find the slope of a line through the points (2,6) and (7,4). 
6-4 



The slope is: m 



2-7 



To Do This on the TI-83 Plus 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Calculate the slope. 


Q6B4Q0 
CD2B7D] 

IENTERI 








C6-4)/C2-7) 

-.4 




3. Change the fraction to a decimal. 
Use the ►Frac function on the |MATH| 
MATH menu. 


|MATH] 1*Frac 

IENTERI 










<6-4V<2-7) 

-.4 
Fins ►Frac 

-2/5 





To Do This on the TI-73 


Press 


Display (Ti-73 shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Calculate the slope. 


CD6B4mE] 

CD2B7[I] 
IENTERI 










C6-4VC2-7> -.4 


3. Change the decimal to a fraction. 












|F«»D| IENTERI 




C6-4VC2-7> -. 
-.4>F**D 


4 

_2 

£ 




4. Simplify the fraction. 

Note: The mode setting ManSimp must be 
selected first. For more information, see § Tip 2: 
Adjusting Your Calculator Settings. 


Node] yyyy 

\±\ to ManSimp 

IENTERI 












<6-4V<2-7) -. 
-.4>F**D 1- 


4 
H 

It) 
.2 

£ 




ISIMPI IENTERI 






5. Use Ovb] to enter the problem. 


[§D6B4 












fi-H 
2-7 


.2 
£ 




|b/c| 2 |-|7 IENTERI 













Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-12 



Chapter 3: Linear Functions Name 

Section 2: Slope Using Coordinates Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Additional Problems 

6-4 
1. Calculate the same problem, m = , on the calculator from the Home screen, using the 

following keystrokes: 
6 R 4 F1 2 R 7 fENTERl 
Did you get the same answer? If not, why not? Which answer is correct? 



2. Find the slope of the line containing the given points using the calculator. Who can do these 
problems faster, the calculator or you? You can also pair with another student and challenge 
each other to see who is faster at the calculations. Write your calculations and answers. 

a. (3,-4) and (-2,8) 



b. (-12,17) and (5,-6) 



c. (36,6) and (-25,6) 



(1.36,2.54) and (1.36,5.72) 



Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 3-13 



Chapter 3: Linear Functions Section 2: Slope Using Coordinates 



Linear Functions: Slope Using Coordinates Teacher Notes 




Objectives 

• To introduce slope as a ratio as the change in y to the change in x. 

• To find the slope of a line using the slope formula. 

• To illustrate the characteristics of lines with positive, zero, negative, or undefined slope. 

• To associate increasing, horizontal, decreasing, or vertical with the appropriate slope. 

Math Highlights 

This section again highlights a review of slope as the steepness of a line. The section opens with 
a bike riding along a piecewise linear path. Students see the definition of slope as a ratio. 

rise change in y y 2 - y t 

Slope = m = = ; = - _ 

run change in x x 2 -m 

Several examples of the calculations are shown. Next, the characteristics of lines with positive, 
zero, negative and undefined slopes are summarized. 

Common Student Errors 

• Many students are concerned that they have to know which point is (x x y t ) and which point 
is (x 2 ,y2). Show that both calculations give the same answer. In the second example below, 
some students are confused when they see division with two negative numbers results in a 
positive slope. Discuss this. For the line containing the points (0,0) and (10,2), the slope is 
calculated by: 

2-0 1 0-2-1 1 

■ = — or 



10 - 5 0-10-5 5 

• Watch for an incorrect substitution where students switch the order in the numerator or 
denominator. For the example above, 

0-2 2-0 

Incorrect: or 



• 



• 



10-0 0-10 

This is a good opportunity to open a discussion on different representations of the same 
number. Students might write a calculator answer without thinking about whether or not the 
representation is the best for the problem. Ask when it is most useful to have the slope 
represented in decimal form versus in fraction form. 

Remind students that they need to use the Order of Operations rules. 

In the (D Try-It!™ section, the correct calculation is (6 - 4) -=- (2 - 7), not 6 - 4 -=- 2 - 7 (where 
division would be performed before subtraction). 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 3-14 



Chapter 3: Linear Functions 



Section 2: Slope Using Coordinates 




Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand mathematical concepts relating to finding the slope 
using graph coordinates. 

If necessary, tell students how to find the Observations for this section. 

Observation 1 

Is any set of three points collinear? 

Three points may be collinear, but are not necessarily collinear. 



urite An observation 



ISftnV JET nF THREE 
PDinTS CDLLinEAR? 



URITE THE ARSHER 
DR YOUR WORKSHEET. 



DID YDU nUTICE . 



THREE F-ninTS ARE HOT 
ALUAYS CDLLinEAR. 



no yes na 



DID YDU riUTICE . 



TUD PDinTS ARE 
ALUAYS CDLLinEAR. 



YES YESy YES* 



FIAD THE SLOPE DF THE 
LIRE THROUGH (2j31fc(-HjHl 
UHKH IS CORRECT ? 

-:_? or... 



Observation 2 

Find the slope of the line through (2,3) and ("4,8). 

Students can pick either point as (x h yj) and (x&yg) to compute the 
slope using the formula. 



DID YDU riUTICE . 



RUTH CALCULATORS GIVE 
THE SAKE SLOPE ! 



0-3 _i£__£ 

"1-2 " "fi " b 
3-0 _ -S _.E 



SAKE 
SLOPE 



2-(-11 *6 6 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-15 



Chapter 3: Linear Functions 



Section 2: Slope Using Coordinates 



Activities 



SELECT fln ACTIVITY 



r 



1. SCREED CR*DSs1 



FiriD THE SLOPE 
P-ETHEER THE GI'.'ETl 

EriDF-niriTS. 



SELECT £ PRESS [ERTER] O 



Scoring: Students get two 
attempts to solve each 
problem. They earn 2 points 
for a correct answer on the 
first try, 1 point for a correct 
answer on the second try. 

Students can earn up to 1 
points. 



Screen Cross 

Tell students to: 

1. Read the directions on the screen, and then press any key to 
continue. 

Note: Repeat steps 2 and 3 for line segments 2 through 5. 

2. Calculate the slope between the two points. Record their work. 

3. Press or to view the choices for the slope (UNDEF = 
undefined slope). When they think the correct slope is 
displayed, press |EIMTER| . Record the endpoints and slopes for 
each segment. The segments are different on each calculator 
and each time the game is played. 

4. Record their final score. 





| SELECT An ACTIVITY I 


^ 


1 LIRKED 

1 CALCULATORS 




L=1=J 




2. SCREER CRDSS 








FIRD THE SLDPE 
BETHEER THE GIVER 
ERDPDIRTS. 




SELE 


C 


T £ PRESS [ERTER] ^ 


& 



Scoring: There are no 
points awarded in the linked 
version. Students must 
answer correctly before the 
next line segment is shown. 

The player who reaches the 
right side of the screen first 
wins. 



Linked Calculators Screen Cross 

Tell students to: 

1. Connect two similar calculators using a unit-to-unit cable. 

2. Try to determine as quickly as possible the slope of the line 
segment. 

3. Select the slope as they did in Screen Cross. 

4. The player who reaches the right side of the screen first wins. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-16 



Chapter 3: Linear Functions Section 2: Slope Using Coordinates 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Students investigate how to input the calculation for slope on the Home screen. See the Student 
Worksheet for instructions. 

Warn students about the correct use of parentheses. They need to be reminded of the Order of 
Operations rules. Notice that the TI-73 has stacked fraction capabilities; therefore, the 
calculation is performed correctly without parentheses. 

Additional Problems 

1. Students input 6-4/2-7 in the calculator. The calculator computes 6 - (4 -=- 2) - 7 = _ 3 since 
division is performed before subtraction according to the Order of Operation rules. This is 
not the correct answer. Students need to be aware that parentheses, such as (6 - 4) -=- (2 - 7), 
override the Order of Operation rules. 

2. Students practice calculating the slope using the calculator, but remind students that they 
can compute these answers faster than the calculator can! Pair students and challenge them 
to try to beat the calculator. 

a. (3,-4) and (-2,8) 



b. (-12,17) and (5,-6) 

c. (36,6) and (-25,6) 

d. (1.36,2.54) and (1.36,5.72) 



slope = 


12 

5 


slope = 


23 
17 


slope = 


= 


slope - 


= undefined 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 3-17 



Chapter 3: Linear Functions Name 

Section 3: Slope as Rate of Change Date 



Linear Functions: Slope as Rate of Change Student Worksheet 

Overview 

The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate mathematical concepts relating to finding the slope using graph 
coordinates. Scroll through the Observations using |T) ([JJ to review, if necessary). Read each 
screen carefully. When you come to a Write an Observation screen, stop and write the answers to 
the questions on your worksheet. 



■■ift««ia.i«JMKiiiim 



HHflT HiriD DF GRAPHS 

have a nnncnnsTflm 

RATE DF CHARGE? ^ 



What kinds of graphs have a nonconstant rate of change? 



Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 3-18 



Chapter 3: Linear Functions 
Section 3: Slope as Rate of Change 



Name 
Date 



Activities 

The Activities section helps you practice finding a slope as rate of change. You can select from 
two activities — Balloon Speed or Dive. Follow these steps to play the activity and complete your 
worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press |ENTER| . 



5 



HflETCHHH 



BflLLDDR SPEED] 



COMPUTE THE 
RATE DF CHARGE 
DF THE BHLLDDH 
DH EACH SEGHERT! 



SELECT £ PRESS [ERTER] O 



Scoring: You get two 
attempts to solve each 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You can earn up to 10 
points. 



Balloon Speed 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press IENTERI to select it. 

2. Select whether you want to play during Nighttime or Daytime. 

3. Take a trip in the balloon. Record the times and positions in 
the table. 

4. Calculate the rate of change (the slope) of each trip, showing 
all work, including the correct units. Enter the rate and press 
IENTERI. If the answer is incorrect, the correct answer is 



displayed; press any key to resume play. 

5. What level did you play? 

6. What was your score? 



Trip 


Start 
Time 


Start 
Position 


Stop 
Time 


Stop 
Position 


Speed 
(include units) 


1 












2 












3 












4 












5 













Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-19 



Chapter 3: Linear Functions 
Section 3: Slope as Rate of Change 



Name 
Date 



Activities (continued) 



SELECT AA ACTIVITY 



FiriD THE CDASTAAT 
RATE DF CHARGE 
DF THE SUBHARIAE 
DA EACH SEGHEAT 



DIVE 



D & 



SELECT $. PRESS [EATER] O 



Scoring: You get one 
attempt to select the 
correct row. If you select 
an incorrect row, the 
correct row is identified. 



Dive 



1. Take a dive in the submarine. Record the times and positions 
in the table below. 

2. Calculate the rate of change (slope) of each segment in the 
table below. Show all your work. Include the correct units. 

3. After the third segment, the next screen displays three rows 
of three rates. Use your rate answers from the table to 
determine the correct row. To select a row, press or to 
move the submarine cursor, and then press IENTERI . 

4. Did you select the correct row? 



Segment 


Start Time 


Start 
Position 


Stop Time 


Stop 
Position 


Speed 
(include units) 


1 












2 












3 













Car Trip Word Problem 

A car takes a 20-minute trip. The car starts at home, (0,0). It travels 
6 miles in 10 minutes. The car stops in traffic for 5 minutes. The 
driver forgot something at home so the car returns in 5 minutes. 
Draw a straight-line graph of the trip. Write the rate of change for 
each leg of the trip on the graph to the right. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-20 



Chapter 3: Linear Functions 
Section 3: Slope as Rate of Change 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus 

See the section on Slope Using Coordinates to find out how to use your calculator to find the 
slope of a line containing two given points. Review the keystrokes. Use these keystrokes to 
compute the rate of change for each pair of data points given. Include the correct units with your 
answer. 



1. 



x (seconds) 


y (feet) 


10 


6.72 


20 


8.05 



2. 



x (hour) 


y (phone calls) 


2 


18 


4 


25 



Rate of Change 



Rate of Change 



3. A space shuttle has an average velocity of 25,405 ft/sec. The velocity of a car on a highway 
can be 60 mi/hr. To find out how many times faster the space shuttle travels compared to the 
car, you must convert the speed of the space shuttle to miles per hour. First, look at the 
conversion by hand, and then do it on the calculator. When set to Float, the calculator shows 
the answer to five decimal places. 

ft 60 sec 60 min 1 mi mi 

25,405 x x x = 17321.59091 — 

sec 1 min 1 hr 5280 ft hr 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. If necessary, exit the Topics in 
Algebra 1 application and clear the 
Home screen. 


[2nd] [QUIT] 




(EXIT)ICLEARI 


2. Calculate 25,405 x 60 x 60 / 5,280. 


25405[x]60[x]60[±] 

52 80|EI\ITER| 










25405*60*60/5230 
17321.59091 











3. How many times faster does the space shuttle travel compared to the car? 

Additional Problems 

Try these by hand, and show your work below. Then check the answers on your calculator. 



5280 feet = 1 mile 
60 seconds = 1 minute 

1. 55 miles/hour -> feet/second 



1000 meters = 1 kilometer 
60 minutes = 1 hour 



2. 35 meters/second -» kilometers/hour 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-21 



Chapter 3: Linear Functions 
Section 3: Slope as Rate of Change 



Name 
Date 



1 Try-It!™ on Your TI-73 

See the section on Slope Using Coordinates to find out how to use your calculator to find the slope 
of a line containing two given points. Review the keystrokes. Use these keystrokes to compute the 
rate of change for each pair of data points given. Include the correct units with your answer. 

1. 



x (seconds) 


y (feet) 


10 


6.72 


20 


8.05 



x (hour) 


y (phone calls) 


2 


18 


4 


25 



Rate of Change 



Rate of Change 



3. A space shuttle has an average velocity of 25,405 ft/sec. The velocity of a car on a highway 
can be 60 mi/hr. To find out how many times faster the space shuttle travels compared to the 
car, you must convert the speed of the space shuttle to miles per hour. First, look at the 
conversion by hand, and then do it on the calculator. When set to Float, the calculator shows 
the answer to five decimal places. 



ft 60 sec 60 min 

25,405 x x 

sec 1 min 



1 mi mi 

x = 17321.59091 — 

1 hr 5280 ft hr 



To Do This 


Press 


Display (TI-73 shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Enter the velocity, 25,405 on the 
Home Screen. 


25405 










25405 




3. Open the CONVERSIONS menu, and 
select the category, Speed. 


[2nd] [CONVERT] 
7:Speed 










:si]!wa:Mii]!e 




1 : Length... 

2: Area... 

3:Uolurie... 

4: Tine... 

5: Temp... 

6:Mass/Weight... 

BflSpeed... 








4. Select the units you are converting 
from, ft/sec. 


1 :ft/sec 










3:ni/hr 
4: kn/hr 
5: knot 










5. Select the units you are converting to, 
mi/hr. 

25,405 ft/s rounded to tenths is 
17321.6 mi/hr. 


3:mi/hr 










25405 ft/sH*ii/hr 
17321.59091 




IENTERI 



6. How many times faster does the space shuttle travel compared to the car?_ 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-22 



Chapter 3: Linear Functions Name 

Section 3: Slope as Rate of Change Date 



i Try-It!™ on Your TI-73 (continued) 
Additional Problems 

Try these by hand, and show your work below. Then check the answers on your calculator. 

5280 feet = 1 mile 1000 meters = 1 kilometer 

60 seconds = 1 minute 60 minutes = 1 hour 

1. 55 miles/hour -> feet/second 



2. 35 meters/second -» kilometers/hour 



Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 3-23 



Chapter 3: Linear Functions Section 3: Slope as Rate of Change 



Linear Functions: Slope as Rate of Change Teacher Notes 




Objectives 

• To associate the slope of a straight line with a constant rate of change. 

• To calculate the rate of change from data points on a line, using the correct units. 

• To read from a linear graph: the rate of change, the scale of the axes, and the correct units. 

Math Highlights 

This section highlights the use of the slope formula to find the rate of change from graphs and 
data. Students may need to review the slope formula; see previous sections on the calculator. 

rate of change = m= - — — units 

X 2 Xj 

Emphasize the use of appropriate units. For example, in the Fill the Pool example in the 
Overview, the students see a pool filling at a constant rate of change. Two data points from the 
growth graph or table shown are (4,2) and (6,3). To find the slope, students should calculate: 

3 - 2 ft 1 ft ft 

rate of change = m = = = .5 — 

6 - 4 hr 2 hr hr 

Mention to students that if the graph of a real problem were nonlinear, the calculation of the rate of 
change using two data points gives the average rate of change over the interval chosen. 

Common Student Errors 

• Neglecting to write the appropriate units. 



• 



• 



Misunderstanding how to use the position with respect to a starting place rather than 
distance. In the slope formula, y 2 -yi gives the signed distance traveled. 

Specifying which point is (x^yj and which point is (x 2 ,y 2 ). Show students that both 
calculations give the same answer. Some students are confused when they see a division by 
two negative numbers that results in a positive growth. Discuss this with the students. Watch 
for an incorrect substitution where students switch the order in the numerator or 
denominator. For example, if the data points (0,0) and (10,2) give the growth of a plant in cm 
per day, the rate of change is calculated: 

2-0 cm 1 cm 0-2 cm _ 1 cm 

Correct: = or 



Incorrect: 



10-0 day 5 day 0-10 day ° day 

0-2 cm 
10-0 day 



• 



Students need to be exposed to other variables besides x and y. For example, it is useful to 
use t for time and d for distance. 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 3-24 



Chapter 3: Linear Functions 



Section 3: Slope as Rate of Change 



Student Worksheet Notes with Answers 




Overview 

Tell students: 

1. How to find the Overview or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand mathematical concepts relating to finding the slope 
using graph coordinates. 

If necessary, tell students how to find the Observations for this section. 

Observation 1 



HRITE RR DBSERYRTIDR . 



HHliT HiriD DF GRAPHS 

have a adacdastaat 
rate df charge? ^ 



Students see the answer 
on the screen at the right. 



What kinds of graphs have a nonconstant rate of change? 
Students write their answer on their worksheet. 

Nonlinear graphs have a nonconstant rate of change. 



DID YDU ADTICE . 



NONLINEAR 
GRAPHS 
hm'.'e a adacdastaat 
rate df chaage. ^ 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-25 



Chapter 3: Linear Functions 



Section 3: Slope as Rate of Change 



Activities 





| SELECT AA ACTIVITY | 








Of 


P-ALLDDASPEEDl 




CDHPUTE THE 
RATE DF CHARGE 
DF THE P-ALLDDA 
DR EACH SEGHERT! 




SELECT i. PRESS [ERTER] O 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

Students can earn up to 
10 points. 



aaEUHBH 



FIRD THE CDRSTART 
RATE DF CHARGE 
DF THE SDBHARIRE 
DR EACH SEGHEAT 



DIVE 



D & 



SELECT i. PRESS [ERTER] O 



Scoring: You get one 
attempt to select the 
correct row. If you select 
an incorrect row, the 
correct row is identified. 



Balloon Speed 

Tell students to: 

1. Highlight a level (bronze = least difficult; gold = most 
difficult), and press IENTERI to select it. 

2. Select whether they want to play during Nighttime or Daytime. 

3. Take a trip in the balloon. Record the times and positions in 
the table. 

4. Calculate the rate of change (the slope) of each trip, showing 
all work, including the correct units. Enter the rate and press 
|ENTER|. If the answer is incorrect, the correct answer is 



displayed; press any key to resume play. 

5. Record the level they played. 

6. Record their score. 

Dive 

Tell students to: 

1. Take a dive in the submarine. Record the times and positions 
in the table below. 

2. Calculate the rate of change (slope) of each segment in the 
table on the worksheet, showing all their work, including the 
correct units. 

3. After the third segment, the next screen displays three rows 
of three rates. Students use their rate answers from the table 
to determine the correct row. To select a row, press or 
to move the submarine cursor, and then press IENTERI . 

4. Record whether they selected the correct row. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-26 



Chapter 3: Linear Functions 



Section 3: Slope as Rate of Change 



Activities (continued) 
Car Trip Word Problem 



Distance 


Rate 


(0,0) to (10,6) 


.6 mi/min 


(10,6) to (15,6) 


mi/min 


(15,6) to (20,0) 


-1.2 mi/min 



HI 




10 IE 



mn 



Notice that the rate is positive going away from home. The rate is negative on the return part of 
the trip indicating the direction of going back home. 

1 Try-It!™ on Your TI-83 Plus or TI-73 

Note: There is a (§ Try-It for the TI-83 Plus and one for the TI-73; they are on separate pages. 

Students review using the calculator to compute the slope of a line containing two points. They 
also see how to use the calculator to do conversions. The TI-73 has conversion functionality 
whereas users of the TI-83 Plus have to know how to set up the conversion. See the Student 
Worksheet for instructions. 

1. 0.1 33 ft per sec 

2. 3.5 phone calls per hour 

Have students discuss the meaning of the rates and their choice of representation. For example, 
is 3.5 phone calls per hour the most meaningful way of communicating the rate of change or is 7 
phone calls every two hours a better way of describing the rate? Have students justify their 
reasoning. 

3. (TI-83 Plus) or 6. (TI-73) 

The space shuttle travels 288. 7 times faster than a car (17321.59091 m/hr -f 60 mi/hr). 

Calculator Problems 

Tell students to follow the steps exactly on the calculators. Example screens are displayed on 
the worksheets for students to compare with the calculator screens. 

Additional Problems 

Students work problems by hand and check on calculator. 



1. 



80 



2_ft_ 
3 sec 



80.6 



ft 



sec 



2. 



126 



km 

hr 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-27 



Chapter 3: Linear Functions 
Section 4: Slope- Intercept Form 



Name 
Date 



Linear Functions: Slope-Intercept Form 



Overview 




Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate mathematical concepts relating to writing slope in slope-intercept 
form. Scroll through the Observations using |T| (|T| to review, if necessary). Read each screen 
carefully. When you come to a Write an Observation screen, stop and write the answers to the 
questions on your worksheet. 



hrite An n&SERYATinn 



|3x * Hy =B| 

is a lire in 

STANDARD FDF;M. 
USE ALGEBRA TD URITE 
THIS LITlE in THE FORM 



nnvnuF; worksheet. 



Observation 

Use your algebraic knowledge to change 3x + 4y = 8 to the form 
y = mx + b. Show your work. 

Remember: 3x + 4y = 8 is Standard Form. 



Activities 

The Activities section helps you practice using the slope-intercept form of lines. You can select 
from two activities — Match It! or Line Soccer. Follow these steps to play the activity and 
complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press |ENTER| . 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-28 



Chapter 3: Linear Functions 
Section 4: Slope- Intercept Form 



Name 
Date 



Activities (continued) 





| SELECT fln ACTIVITY | 


__■ 




Of 

Tj 


HATCH IT! 1 




U.llttH.lfel 

V- ffl 




SELECT i. PRESS [ENTER] 


O 



Scoring: You get two 
attempts to answer the 
problem. You earn 2 
points for a correct 
answer, 1 point for a 
correct answer on the 
second try. 

You can earn up to 12 
points. 



n 



gaEJBHBH 



LIRESDCCERl 



CHALLENGING 

ouESTinns using 



SELECT $. PRESS [ENTER] O 



Scoring: You get two 
attempts to answer the 
problem. You earn 2 
points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. 

You score a goal when 
you answer a question 
correctly against Alex, the 
goalkeeper. You also get 
to keep any points you 
earned while passing the 
ball. 



Match It! 

1. Select the correct answer to the question. Questions include: 

• Selecting the graph that correctly illustrates an equation. 

• Selecting the equation that correctly describes a graph. 

• Selecting the equation that goes with the table. 

2. What was your score? 



Line Soccer 

1. Pass the ball by answering a question correctly. Possible 
slope-intercept questions include: 

• Selecting the (x,y) coordinate that solves an equation. 

• Using an (x,y) coordinate and b to solve for m in an 
equation. 

• Using an (x,y) coordinate and m to solve for b. 

• Using two (x,y) coordinates to calculate m and b. 

2. To enter your answer: 

• As a negative number, press [O- 

• As a mixed number, enter the whole number and press 
(UNIT), and then enter the fraction. 

• As a fraction, press (n/d) and enter the numerator. Press 
(n/d) again and enter the denominator. 

3. Show your work for each problem: 



4. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-29 



Chapter 3: Linear Functions 
Section 4: Slope- Intercept Form 



Name 
Date 



Activities (continued) 
Additional Problems 

1. Make a table and draw the graph for the following linear functions, 
a. Y = -X + 2 b. Y = 2X - 1 



X 



X 



2. Think of the graph below as a map. You start to walk from the point ("1,1). You can walk only 
along a path that is the line with the slope: m = "2 



a. Label two points, A and B, that you can walk to 
on the graph if the slope of your path = _ 2. Each 
tick mark is 1 unit. 

b. Find the equation of the line that describes your 
walking path. Show your work below. 



c. Record the coordinate points of A and B below. 
Use the equation of your path to check to see if 
your points A and B are on really on your line! 
Show your work below. 



Point 


Check It 


A= 




B= 





Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-30 



Chapter 3: Linear Functions 
Section 4: Slope- Intercept Form 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Parent and Family of Functions 

Compare graphs of Yi =X and Y2=X+1 . If you know the graph of Yi =X, can you draw the graph of 
any line in slope-intercept form? Investigate using your calculator! 

Note: See § Tip™ 3: Graphing a Function and § Tip™ 5: Adjusting the Viewing Windowior instructions if you need help. Set up your 
calculator so that GridOn on the window format ( [Ml [format]) screen and ZDecimal on the zoom menu ( |zoom| ) are selected. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. Define Yi=X and Y2=X+1 . 

Note: On the TI-73, use pel rather than |x,T,e,n|. 










|Y=| ICLEARI 




Noti Not2 Plots 
WlBX 

WzHX+1 




|X,T,0,n| 


I -I ICLEARI 
|X,T,0,n||+l 1 








3. Set the viewing window. 


TI-83 Plus: 










BMMj MEMORV 
TTZBox 
2: Zoom In 
3: Zoom Out 
SpZDecinal 
5:ZS^uare 




|Z00M| 4:ZDecimal 

TI-73: 


(ZOOM) 8:ZDecimal 




4. Trace both Yi and Y2. 










ITRACEI 

{*} or UJ to trace a 

function 

and to move 

between functions 




V1=K 


^ 




K=0 / 


v=o 









5. Write a description of what you see. How does the graph of Y=X compare to the graph of 
Y=X+1? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-31 



Chapter 3: Linear Functions 
Section 4: Slope- Intercept Form 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



To Do This 


Press 


Display (TI-83 Plus shown) 


6. Enter and trace Y3=X-1 . 

Note: On the TI-73, use pel rather than |x,T,e,n|. 


m 










Noti PlotZ Plots 

WiBX 
WzBX+1 
WsBX-1 
Wh = 
We = 
Ws = 




MMICLEARI 

|x,T,e,/7|Ld 1 

ITRACEI 

{*} or UJ to trace a 

function 

and to move 

between functions 



























7. Write a description of what you see. How does the graph of Y=X compare to the graph of 
Y=X-1? 



8. Where will the line, Y=X+2 be located? Draw in your prediction 
and then use the calculator to check your work. Was your graph 
correct? If not, why not? 


























9. Now predict and draw the following lines on the graph to your 
right. Draw your own axes. Do not use the calculator. 

Y=X+3 
Y=X-3 
Y=X+8 
Y=X-8 































10. Check your work! Graph each line on the calculator. Could you see all of the lines? Record 
your observations. 

Note: On the TI-73, you need to clear a line in the Y= editor to make room for your new lines. 



11. You cannot see Y=X+8 or Y=X-8 on your graphing calculator. Why do you think that the line is 
not showing? Change your WINDOW ( IWINDOWD settings so that you are able to see these lines. 
Record the changes you made. 



12. Compare the lines: Y=X, Y=2X, and Y=3X. What do you notice? Try other lines in the form 
Y = AX. Next, try to graph Y=2X+3 without the calculator. Explain your strategy. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 3-32 



Chapter 3: Linear Functions Section 4: Slope-Intercept Form 



Linear Functions: Slope-Intercept Form Teacher Notes 




Objectives 

• To review the form of the equation y = mx + b, where m is slope and b is the y-intercept. 

• To view graphing lines and developing equations from data. 

• To view tables of values and graphing lines from an equation of the form y = mx + b. 

• To emphasize three ways of looking at lines, tables, graphs and equations. 

• To develop the equation of a line from information given, such as slope and y-intercept, point 
and slope, and two points. 

• To review the slope of parallel and perpendicular lines. 

Math Highlights 

This section highlights a review of the slope-intercept form of a line, y = mx + b. Students will 
review graphing a line using one point and the slope of the line. They will also see the equation of 
a line developed inductively from data by simulating the amount of volts produced by lining up 
batteries in series. Students will also review how to find a table and graph a line using the 
equation y = mx + b. 

A review of calculations follow, which show the step-by-step procedures needed to find the 
equation of a line given, the slope and y-intercept, the slope and a point on the line, and finally 
two points. 

Common Student Errors 

• When students perform the calculations to find the equation of a line given the slope and 
y-intercept, the slope and a point on the line, or two points, they often have problems 
following the steps. For example, given two points, the student needs to perform three steps. 
First, the student needs to calculate the slope of the line. Students may forget the formula for 
slope, and then be careless about substituting the correct values in the formula. Also, they 
may make errors in sign. In the second step, they need to find b using the calculated slope 
and one of the points. Students need to understand that they could pick either point for this 
calculation. If the slope is incorrect from the first step, the error cascades into the rest of the 
solution. In the third step, they need to place all of the information into the final answer as 

y = mx + b. 

• Students become comfortable using the variables x and y. They should be exposed to the use 
of other letters for the independent and dependent variables. Students should be able to 
recognize, for example, D = 2T + 4 as a linear relationship with independent variable T, 
dependent variable D, a slope of 2 and the D-intercept as 4. They need to learn that they will 
need to change the variables so the function reads y = 2x + 4 in order to graph it on the 
calculator. 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 3-33 



Chapter 3: Linear Functions 



Section 4: Slope-Intercept Form 




Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand using algebra to change a linear equation in standard 
form to slope-intercept form. 

If necessary, tell students how to find the Observations for this section. 

Observation 

Students use algebra to write 3x+4y=8 in y=mx+b form. 



HRITE fln DBSERYHTinn . 



|3X * ny =B| 

is H LinE in 

JTiiriDiifiD FDRH. 
USE RLGEBRR TD HRITE 
THIS LIRE IR THE FDRH 



Dn YDUR UDRKSHEET. h> 



Answers may vary, especially the step order. One possible 
answer: 

Step 1: Subtract 3xfrom both sides of the equation. 
3x - 3x + 4y = 8 - 3x 

Step 2: Simplify the equation. 

4y = -3x + 8 

Step 3: Divide both sides of the equation by 4. 
4y -3 8 

Step 4: Simplify to get the answer. 
-3 



y = T 



x + 2 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-34 



Chapter 3: Linear Functions 



Section 4: Slope-Intercept Form 



Activities 





| SELECT An ACTIVITY | 


__■ 




Of 

Tj 


HATCH IT! 1 




li.|ir;^.|,H 

V- ffl 




SELECT i. PRESS [ENTER] 


O 



Scoring: Students get 
two attempts to answer 
the problem. They earn 2 
points for a correct 
answer, 1 point for a 
correct answer on the 
second try. 

Students can earn up to 
12 points. 



n 



gaEJBHBH 



LIRESDCCERl 



CHALLENGING 

ouESTinns usinc 



SELECT $. PRESS [ERTER] O 



Scoring: Students get 
two attempts to answer 
the problem. They earn 2 
points for a correct 
answer, 1 point for a 
correct answer on the 
second try. 

Students score a goal 
when they answer a 
question correctly against 
Alex, the goalkeeper. 
They also get to keep any 
points they earned while 
passing the ball. 

Note: Unsimplified 
fractions are counted as 
correct. 



Match It! 

Tell students to: 

1. Select the correct answer to the question. Questions include: 

• Selecting the graph that correctly illustrates an equation. 

• Selecting the equation that correctly describes a graph. 

• Selecting the equation that goes with the table. 

2. Record their scores. 



Line Soccer 

Tell students to: 

1. Pass the ball by answering a question correctly. Possible 
slope-intercept questions include: 

• Selecting the (x,y) coordinate that solves an equation. 

• Using an (x,y) coordinate and b to solve for m in an 
equation. 

• Using an (x,y) coordinate and m to solve for b. 

• Using two (x,y) coordinates to calculate m and b. 

2. Enter their answers in the following ways, as necessary: 

• as a negative number, press O- 

• as a mixed number, enter the whole number and press 
(UNIT), and then enter the fraction. 

• as a fraction, press (n/d) and enter the numerator. Press 
(n/d) again and enter the denominator. 

3. Show their work for each problem. 

4. Record their scores. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-35 



Chapter 3: Linear Functions 



Section 4: Slope-Intercept Form 



Activities (continued) 
Additional Problems 

1. Students make a table and draw the graph for Y= _ X+2 and Y=2X-1 . 

Answers may vary. Make sure that students correctly label the axes and all points from the 
corresponding table. 

2. Students label two points, A and B, where the line segment between the two has a slope that 

is -2. 

a. Possible points students can walk to on the screen shown are ("2,3), (0, _ 1), and (1,"3). 

b. Students should use m-~2 and the point; for example, ("1,1) to find the y-intercept, b. 
The answer is y-~2x-l. 

c. Students should substitute their point in the line to see if the equation is satisfied. 

1 Try-It!™ on Your TI-83 Plus or TI-73 

Students need to know the features of the calculator covered in (J) Tip™ 3: Graphing a Function 
and fj) Tip™ 5: Adjusting the Viewing Window. They work through an investigation of parent 
and family of functions of Y=X. See Student Worksheet for details. 

Tell students to follow the steps exactly on the calculators. Example screens are displayed on 
the worksheets for students to compare with the calculator screens. 

This keystroke exercise lets students discover the connection between the parent and family of 
functions so they can quickly graph functions of the form y=mx+b. 

5. Possible answers for comparing the graph of Y=X to Y=X+1 : parallel, equivalent slope, offset 
by 1, Y=X crosses the origin (0,0), etc. 

7. Possible answers for comparing the graph of Y=X to Y=X-1 : same as above. 

8. Students should draw the function on the worksheet first before graphing it on the 
calculator. Y=X+2 intersects the X-axis at (~2,0) and the Y-axis at (0,2). 



VH=K+2 




K="2 


V=0 



VH=K+2 



K=0 



■> 



V=2 



10. Students should draw the function on the worksheet first before graphing it on the 

calculator. If they graph it without changing the window values, the screen looks like this: 




Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-36 



Chapter 3: Linear Functions 



Section 4: Slope-Intercept Form 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Parent and Family of Functions 

11. Students cannot see all functions when they don't change their window values, which are: 
Xmin=-4.7, Xmax=4.7, Xmin=-3.1, Xmax=3.1. To fit all functions on the screen, Xmin>8 and 
Xmax>8. Functions in order from top to bottom: Y=X+8, Y=X+3, Y=X-3, Y=X-8. 




12. In order from top to bottom: Y=3X, Y=2X, Y=X (ZFit window values). Graph of Y=2X+3 
(ZStandard window values). To graph the function Y=2X+3, students should think that the 
graph is parallel to Y=2X, and then shift Y=2X up 3 units on the Y-axis. 





Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



3-37 



Chapter 4: Linear Inequalities 
Section 1 : Using Graphs & Tables 



Name 
Date 



Linear Inequalities: Using Graphs & Tables 



Overview 



Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) (|TJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate mathematical concepts relating to inequalities. Scroll through the 
Observations using (TJ (JJJ to review, if necessary). Read each screen carefully. When you come 
to a Write an Observation screen, stop and write the answers to the questions on your worksheet. 





1 nBSERYHTinn ... | 


DH YDUR WORKSHEET 






DRAU THE GRAPH DF 
EACH INEQUALITY 


O 







Observation 1 

If x is a real number, draw the number line graph of each 
inequality. Remember to use open and closed notation and to 
label each number line correctly. 

1. x<3 



2. x<3 



x>6 



x>6 



Draw the number line graphs for these inequalities (which are not 
in the Topics in Algebra 1 application). 



5. x>-^ 



6. x<1.25 

< 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-1 



Chapter 4: Linear Inequalities 
Section 1 : Using Graphs & Tables 



Name 
Date 



Activities 

The Activities help you practice using graphs and tables to solve inequalities. You can select from 
three different activities — Build the Solution Set!, Worksheet Activity 1, and Worksheet Activity 2. 

Follow these steps to play the activity and complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press [ENTER]. 



SELECT fln ACTIVITY 



BUILD THE 
2 | SDLUTIDH SET ! 



*+- 



■++ 



3 "2 "i i 2 3 
SELECT i. PRESS [ENTER] O 



Scoring: There are five 
problems in each set. You 
get two attempts to solve 
for x for each problem. 
You get 2 points for a 
correct choice on the first 
try, and 1 point for a 
correct choice on the 
second try. 

You can earn up to 10 
points. 



Build the Solution Set! 

1. Use |3] or UJ to move the cursor along the number line. Press 
IEMTERI to select the first point to test. The point is displayed 
along with the result of the test. 

2. Choose another point to test. After the point and result of the 
test for the second point are displayed, four possible solutions 
for x are displayed. 

3. Press [TJ or |TJ to highlight the correct solution, and then press 
IEMTERI to select it. If you choose an incorrect solution on the 
first try, you get another try. If you choose an incorrect 
solution on the second try, the correct answer is displayed; 
press any key to go to the next problem. As you play the 
activity, write the inequalities and their solutions. 



4. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-2 



Chapter 4: Linear Inequalities 
Section 1 : Using Graphs & Tables 



Name 
Date 



Activities (continued) 





| SELECT An ACTIVITY | 


±\ 




Mr 


PLEASE SEE YDUR 
UDRKSHEET FDR 
HDRE ACTIVITIES. 








O 



Note: Press H or to 
leave this screen. 



Worksheet Activity 1 

Use the number lines below to estimate the solution set of the 
following inequalities. Use number sense to place a scale on each 
number line so that you are able to show the solution set. Check 
several points as shown in the previous activity. Show all of your 
work. 

1. x + 2.5 < 7 



2. x - 3.6 < -2 



q 3.1 

3. x + ^ > 4g 



X 


HI 




■3 


-a.E 




-2 


-s 




-i 


-3.E 







-1 




1 


IE 




£ 


H 




J 


b.E 




V1B2.5X-1 



Worksheet Activity 2 

Use the table of the expression 2.5X-1 at the left to find out when 
2.5X-1 <3. First estimate the answer, and then use number sense 
to determine the exact answer. Write your strategy for the 
solution, and draw the solution set on a number line. 



2.5X-1<3 

< 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-3 



Chapter 4: Linear Inequalities 
Section 1 : Using Graphs & Tables 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 



Solution search using X-Y graphs: Find the solution set for the inequality X-1<1. Before you start, 
estimate the solution using number sense. Write your estimate here. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 



[2nd] [QUIT] 
(EXIT) [CLEAR] 



2. Set your window format as shown. 

Note: See § Tip™ 5: Adjusting the Viewing Window 
for more information. 



TI-83: 

[2nd] [FORMAT] 
RRR [ENTER] 

TI-73: 

[2nd] [FORMAT] 
R R [ENTER] 



PolarGC 

_ CoordOff 

Qr-idOff H3EIIS 

RxesOTT 

Label On 

xprOff 




3. Enter both sides of the inequality into 
the Y= editor as shown. 

Note: On the TI-73, use \x\ rather than |x,T,o,n| . 

Note: You may need to deselect the other Y= 
functions. See i Tip™ 3: Graphing a Function in the 
Standard Window. 



[Y^I ICLEARI 
|X,T,0,n| R 1 
R lCLEARI 
1 



Noti PlotZ Plots 
WlBX-1 

WzHl 




ofiWB MEMORV 
TTZBox 
2: Zoom In 
3: Zoom Out 
SBZDeciMal 
oTZS^uare 
6:ZStandard 
7-i-ZTrig 



4. Select ZDecimal to set the viewing 
window and graph the functions. 



TI-83: 

[ZOOM] 4:ZDecimal 

TI-73: 

[ZOOM] 8:ZDecimal 



5. Trace the functions. 

Note: The function displays in the upper left corner 
of the screen; the X and Y values are displayed on 
the bottom of the screen. 



ITRACEI 

R or R to trace a 

function 

R and R to move 

between functions 



6. Compare Y1 and Y2 for the same X values. For example, notice 
that when X = -1, Y1= -2 and Y2=1 as shown on the screens. 

Where is X-1 <1? 



7. 



Hint: Trace Y1 to find out when Y1< Y2. 
Why? 



V1=K-i ■ ■ 


■■./. 






K=-i /. 


V=-2- ■ ■ 



V2=i' ' ' 


::/. 






K=-i /. 


V=i ■ ■ ■ 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-4 



Chapter 4: Linear Inequalities Name 

Section 1 : Using Graphs & Tables Date 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Additional Problems 

Solution Search: On the following problems, first estimate the solution using number sense. Then 
search for the solution set for each inequality using graphs as shown in the previous example. 
Finally, draw your graphs from your calculator and show your work. 

Don't forget to set an appropriate viewing window in order to see your graphs. 

Note: See § Tip™ 5: Adjusting the Viewing Window for more information. 
1. 2X+3 < 7 



X+4 > -3 



0.5X-1 < 2 



4. X-2 > -3 



Topics in Algebra 1 © 2001 Texas Instruments Student Worksheet 4-5 



Chapter 4: Linear Inequalities Section 1 : Using Graphs & Tables 



Linear Inequalities: Using Graphs & Tables Teacher Notes 

Objectives 

• To illustrate how to estimate the solution set, in the real numbers, of a linear inequality using 
graphical methods on a number line and on a Cartesian (x-y) graph. 

• To illustrate how to estimate the solution set, in the real numbers, of a linear inequality using 
tables. 

Math Highlights 

In the number line method, students use a guess-and-test approach to search for the solution on 
a number line. A point is chosen to test, the substitution is shown and students see whether the 
statement is true or false. A point is plotted for a true statement. Students see an estimate of the 
solution set built on the number line. 

In the table of values method, students see a table of values for each side of the inequality. They see 
where the inequality is satisfied, and then they see how to refine the estimate of the solution set. 

In the x-y graphical method, students plot both sides of the inequality and use the graph to determine 
the solution set for the inequality by testing points. In the 2-D graph, students are able to see which 
graph is higher or lower than the other graph. This helps them estimate the solution set. 

Note: The inequalities of the form ax + b < c (for <, <, >, >) with a < are not discussed in this 
section. 

Common Student Errors 



• 



• 



• 



Using graphs and tables can mislead students. They may think that they can always find the 
exact solution using graphs and table. Although they will often find exact solutions using 
these methods, using algebra will always give exact solutions for inequalities. For the 
calculator example, x + 2 < 1, only integer values are tested. If the example had been 
x + 2 < 1, the students would need to test points closer and closer to x = _ 1 to see that the 
solution set contains values strictly less than -1. The endpoint (~1) is not included in the 
solution. Encourage students to pick many points. Remind them that they would have to test 
all points with these methods to get the exact solution, in the real numbers and that is 
physically impossible to test all points! 

At times, introducing the algebraic solution of inequalities gives students just the mechanics 
of doing a problem. Algebraic methods alone usually do not invite students to reason out the 
solution using number sense. The graphs and tables method gives students the opportunity to 
see the values of each side of the inequality as a graph or table so they can compare the size 
of the numbers, thus helping them create the solution set. 

Visual learners can benefit by seeing the graphs and numbers and using them as the tool to 
find the solution set. 

Some students may still have difficulty remembering the meaning of the symbols, <, <, >, and 
>. 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 4-6 



Chapter 4: Linear Inequalities 



Section 1 : Using Graphs & Tables 




Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations help students understand concepts about linear inequalities relating to graphs 
and tables. If necessary, tell students how to find the Observations. 





■ .l&MUttH.lflM 


O 


Dn YDUR WORKSHEET 




DRAU THE GRAPH DF 
EACH INEQUALITY 







Observation 1 



GRAPH y. i 3 j 4!I33il 
+1 1 1 — 9- 



H h* 

i 2 3 H S b 
GRAPH x J 3 fWliHM 

+1 1 1 » 1 1 h+ 

i 2 3 H £ b\ 



GRAPH x > 6 j 4!I33il 

*H 1 1 — 1 — I 1 1+ 

3 H £ b ? H 9 
GRAPH x L b fWliH^J 

n 1 1 — » 1 1 1+ 

3 H £ b ? B 9. 



1. 

2. 

3. 

4. 



x<3 
x<3 

x>6 
x>6 



' -I 



i i.EE i.E i.7E £ 



1 



x > 



(Not in the Topics in Algebra 1 
application.) 

6. x<1.25 

(Not in the Topics in Algebra 1 
application.) 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-7 



Chapter 4: Linear Inequalities 



Section 1 : Using Graphs & Tables 



Activities 



SELECT fln ACTIVITY 



BUILD THE 
2 | SDLUTIDA SET ! 



++- 



■++ 



3 "2 "i i 2 3 
SELECT i. PRESS [EATER] O 



Scoring: There are five 
problems in each set. 
Students get two attempts 
to solve for x for each 
problem. You get 2 points 
for a correct choice on the 
first try, and 1 point for a 
correct choice on the 
second try. 

Students can earn up to 
10 points. 



Build the Solution Set! 



Tell students to: 



1. Use |3] or UJ to move the cursor along the number line. Press 
IENTERI to select the first point to test. The point is displayed 
along with the result of the test. 

2. Choose another point to test. After the point and result of the 
test for the second point are displayed, four possible solutions 
for x are displayed. 

3. Press [JJ or (T| to highlight the correct solution, and then press 
IENTERI to select it. If students choose an incorrect solution on 



the first try, they get another try. If they choose an incorrect 
solution on the second try, the correct answer is displayed. 
Students can press any key to go to the next problem. As they 
play the activity, they should write the inequalities and their 
solutions. 

4. Record their scores. 



n 



ggiUHBa 



PLEASE SEE YDUR 
WORKSHEET FDR 
HDRE ACTIVITIES. 



Note: Students can press 
or UJ to leave this 
screen. 



Worksheet Activity 1 

Tell students to: 

1. Use number sense to estimate the solution set for the 
following three inequalities on the number lines provided. 

2. Place the appropriate scale on each number line so that they 
are able to show the solution set appropriately. 

3. Check several points as shown in the activity above. 

4. Show all of their work. 

1. x + 2.5 < 7 when x < 4.5 



2. x - 3.6 < -2 



when 



x<1.6 



3. 



x + 4>4g 



when 



X>3r 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-8 



Chapter 4: Linear Inequalities 



Section 1 : Using Graphs & Tables 



Activities (continued) 



X 


HI 




-3 


-H.£ 




"2 


-fi 




-i 


-3.£ 







-1 




i 


IS 




2 


H 




5 


fi.E 




ViH2.5X-l 



Worksheet Activity 2 

Tell students to: 

Use the table of the expression 2.5X-1 shown on their worksheets 
(shown at left) to find out when 2.5X-1<3 by first estimating the 
answer, and then using number sense to determine the exact 
answer. Remind them to write their strategy for the solution and 
to draw the solution set on a number line. 



From the table, students should see that they need to test more 
values between X=1 and X=2 to find where 2.5X-1<3. 

If you wish the students to continue the activity on their 
calculators, tell them to enter the function in the Y= editor. Then 
on the TABLE SETUP screen ( 1 2nd I [TBLSET]), they can refine their 
search as shown in the screens below. 

The students see that 2.5X-1 is equal to 3 at X=1.6, but they need 
to figure out when 2.5X-1< 3. Students can go to the TABLE 
SETUP screen and change the settings to TblStart=1 and ATbl=.1, 
and then investigate further. This problem should be discussed 
to show that the search should still continue because the 
endpoint of 1.6 is not in the solution set. The answer is X<1.6. 
To investigate further, refine the table values by changing 
TblStart=1.5, <md ATbl=.01 . 



TABLE SETUP 

TblStart=l 

*Tbl=.l 
Indpnt: EHE flsk 
Depend: IgBIB; flsk 



X 


HI 




1 


IS 




l.i 


1.7S 




1.2 


2 




i.s 


2.25 




i.H 


2.£ 




IS 


2.7E 




i.fi 


3 




V1B2.5X-1 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-9 



Chapter 4: Linear Inequalities 



Section 1 : Using Graphs & Tables 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Solution Search Using X-Y Graphs: Tell students to first estimate the solution for the inequality 
X-1<1 using number sense and then find the solution set using a calculator. 

6. X-1 < 1 when X< 2. 

7. Answers may vary. Students can trace the graph to see the result. 



in 



Additional Problems 

Students investigate inequalities using X-Y graphs to compare numbers in order to create the 
solution set. See the student worksheet for calculator details. Students must set appropriate 
graphing windows in order to see the graphs. Graphing windows shown use |Z00M| ZStandard, 
which sets X and Y values so that "10 < value < 10. 



1. 


2X+3 < 7 
X+4 > -3 
0.5X-1 < 2 
X-2 > -3 




/ 




/ 


A 




C XS2 / 


z 








2. 


-7 ^ 


K>-7 




v r 






y 










3. 










— -"fl 




H<fi__-^ 


b 








4. 


-i 








v- 1 KL-1 ' 




y^ 





Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-10 



Chapter 4: Linear Inequalities 
Section 2: Using Algebra 



Name 
Date 



Linear Inequalities: Using Algebra 



Overview 




Student Worksheet 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using |T) ([JJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate mathematical concepts relating to using algebra in linear inequalities. 
Scroll through the Observations using (T| ([JJ to review, if necessary). Read each screen carefully. 
When you come to a Write an Observation screen, stop and write the answers to the questions on 
your worksheet. 



■■ift««ia.i«JMKmini 

SOLVE FDR :■:: 



-2X+3 < ii 

an vnuF; udrksheet 



Observation 

Solve the inequality. Show your work. 



Draw the solution set on the number line. 
< 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-11 



Chapter 4: Linear Inequalities 
Section 2: Using Algebra 



Name 
Date 



Activities 

The Activities help you practice using algebra to solve inequalities. You can select from two 
different activities — Solve It! and Free Fall. Follow these steps to play the activity and complete 
your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press |ENTER| . 



^SSESESSM 



SOLVE IT ! 



PICK THE CORRECT 
STEPS Tn SOLVE 
THE INEQUALITY. 



SELECT 3. PRESS [EDTER] Q 



Scoring: You get two 
attempts to pick the step. 
You earn 2 points for a 
correct answer on the first 
try, 1 point for a correct 
answer on the second try. 
You get an additional 2 
points for the correct 
solution. 

The total number of points 
available varies. 



Solve It! 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IEMTER] to select it. 

2. Look at the algebraic expression at the top of the screen and 
decide what must be done to solve the inequality for x. 

3. Press or to cycle through steps to choose from, and then 
press |ENTER| to select the correct step (some problems require 
two steps). If your second choice is incorrect, the correct step 
is displayed; press any key to continue play. If the activity 
prompts you to select the correct result, highlight it with or 
0, and then press |ENTER| to select it. As you play the activity, 
write each inequality. What was your strategy for finding the 
solution? 



4. What level did you play? 

5. What was your score? 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-12 



Chapter 4: Linear Inequalities 
Section 2: Using Algebra 



Name 
Date 



Activities (continued) 





| SELECT AH ACTIVITY | 


XI 




Mr 


FREE FALL 1 




UHAT GOES UP.. 
MUST CDHE DDUR 




SELECTS PRESS [ERTER] O 



Scoring: Points are 
based on how quickly you 
solve each equation. 

Unless you specify point 
or time limits for this 
activity, students can play 
the activity when four 
missed equations stack 
up, the game is over.or 
they press (QUIT) to stop. 
There is no time limit. 



Free Fall 

1. Highlight a level (silver = less difficult; gold 
and press IENTERI to select it. 

2. When you are ready to start, press any key. 



more difficult), 



3. Watch the equation as it falls, and quickly solve for x. Enter 
the solution (press O for negative numbers), and press IENTERI 
before the equation hits bottom. If you give an incorrect 
answer, the correct answer is displayed; press any key to 
resume play. The incorrect equation stacks up at the bottom 
of the screen, giving you less time to solve the next equation. 

4. Follow your teacher's instructions for how long to play the 
activity. 

5. What level did you play? 

6. What was your score? 



Additional Problems 

Solve the following inequalities. Show your work. 



1. 6.4x > 16 



2. -x-2<-2 
2 



3. 2x-2.1<-3.5 



A cell phone company charges a flat fee of $15 per month to use the phone. They also charge 
25 cents for each phone call you make no matter how long you are on the phone. Your budget 
allows you to spend at most $30 per month for the phone. How many phone calls will you be 
able to make each month? (Tax is included in the prices.) Show your work. Write a short 
paragraph explaining why would you choose this company or why not. 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-13 



Chapter 4: Linear Inequalities 
Section 2: Using Algebra 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Testing points and graphing solution sets: If X=3, is 2X+4>7 true or false? Try it by hand first. 
Show your work below. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)|CLEAR| 


2. From the Home screen, the calculator 
can tell you if a sentence is TRUE or 
FALSE (1=TRUE and 0=FALSE). 






3. First, check what value is currently 
stored in X. 

Note: On the TI-73, use pel rather than |x,T,e,n|. 






|X,T,0,n| 


I ENTER | 



4. What is the value of X stored in your calculator? 



Check around the class. Most likely, there are many different values of X. 



5. First, if you want to find out if 
2X+4 > 7 is true or false when X=3, 
you must tell the calculator that X=3, 
which is called storing a value in X. 

Note: On the TI-73, use pel rather than |x,T,e,n|. 










ICLEARI 




3*X 

3 




3ISTOMX,T,0,n| 

|ENTER| 


6. Next, input the number sentence 
2X+4>7. This takes two steps. 

Note: On the TI-73, use pel rather than |x,T,e,n|. 










2|X,T,0,/j|| + | 4 




3*X 

3 
2X+4 




7. You can find the > (greater than) sign 
in the catalog ([2nd] [CATALOG]). 

Shortcuts: On the TI-83 Plus, press [2nd] [test] 3. 
On the TI-73, Dress [2nd! [textI RRRPIH IenterI 
to select > and IH Ienteri to select Done. 


[2nd] [CATALOG] 

until the cursor is 

next to > 










CflTflLOG 

< 

► > 

< 

> 




IENTERI 








8. Now, complete the sentence and see 
the result! 

Remember, 1=TRUE and 0=FALSE. If 
you substitute X=3, you get 10>7 
which is TRUE. 


7 










3*X 

3 
2X+4>7 

1 




|ENTER| 









Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-14 



Chapter 4: Linear Inequalities 
Section 2: Using Algebra 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



To Do This 


Press 


Display (TI-83 Plus shown) 


9. Test another point! (Try - 1 .) 

Note: On the TI-73, use pel rather than IX,T,0,nl. 










l(-)l 1 ISTOI |X,T,0,/7| 




3+X 

3 
2X+4>7 

1 
-1+X 

-1 




I ENTER | 








10. You do not have to type in the 
number sentence 2X+4>7 again. 

Note: You also can edit an expression after it is 
pasted to the line. 

Since 1 =TRUE and 0=FALSE, 
2X+4>7 is FALSE when X=-1 . 


TI-83 Plus: 

[2nd] [ENTRY] 
[2nd] [ENTRY] 
I ENTER | 

TI-73: 

SSSSto highlight 

expression 

lENTERltocopy 
I ENTER | 










3 
2X+4>7 

1 
-1+X 

-1 
2H+4>7 













Graph the inequality 2X + 4 > 7. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Graph this solution set. 

Note: On the TI-73, use pel rather than IX,T,e,nl. 










|Y=| ICLEARI 




M*ti M*t2 Plots 

-oViH2X+4>7 




2|X,T,e,n|| + |4 
[2nd] [CATALOG] 
until the cursor is 
next to > 








I ENTER | 
7 




2. Set the graph style to the animate 
graph style, which lets you see the 
graph as it is being plotted, even 
when it is on the axis at Y=0. 


(T| until the cursor is in 
the left column 




1 ENTER 1 until the -0 style 
is indicated 


3. Set the viewing window and graph 
the inequality by selecting ZDecimal. 


TI-83 Plus: 










ofiWB MEMORV 
TTZBox 
2: Zoom In 
3: Zoom Out 
SBZDeciMal 
oTZS^iuare 




|Z00M| 4:ZDecimal 
TI-73: 


|Z00M| 8:ZDecimal 


oJWWB MEMORV 

5tZS^iuare 

6:ZStandard 

7:ZooMStat 

HflZDeciMal 

?:ZooMFit 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-15 



Chapter 4: Linear Inequalities 
Section 2: Using Algebra 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



To Do This 


Press 


Display (TI-83 Plus shown) 


4. Trace the function. Notice that 
where the graph is FALSE, Yi=0; 
where the graph is TRUE, Yi=1 . 










ITRACEI 

H or to trace the 

function 




V1=2K+H>7 

False^ 






.). . . 


n=-.r 


V=0 








5. Notice that Yi =0 (FALSE) up 
through X=1 .5 (when X<1 .5). 


[Tj or |T) to trace the 
function 










V1=2K+H>7 






■I 


K=i.£ 


v=o 








6. Keep tracing and you see that the 
graph jumps to Yi=1 (TRUE) when 
X>1.5. 

Find the exact set using algebra. 
Solve 2X+4>7. Does your answer 
agree with this graph? 


\J\ or |T) to trace the 
function 










V1=2K + H>? Tme 






r - . 


K=3 


V=i 









Additional Problems 

Above, you solved the following inequalities using algebra. Now, graph the solution set of these 
inequalities using your calculator. Compare the graph to your calculated answers above. 

1. 6.4X>16 



2. 2 X_2 ^" 2 



3. 2X-2.1<-3.5 



Topics in Algebra 1 



©2001 Texas Instruments 



Student Worksheet 4-16 



Chapter 4: Linear Inequalities Section 2: Using Algebra 



Linear Inequalities: Using Algebra Teacher Notes 




Objectives 

• To review one-step and two-step linear inequalities. 

• To review the Properties of Inequalities. 

Math Highlights 

This section opens with examples of solving linear inequalities of the forms, x + a < b, ax < b, 
and ax + b < c for any relation <, <, >, and >. Word problems about an amusement park are 
included for students to solve. The students also see the need to interpret the answers obtained 
using the appropriate number set. For example, they find that they have to knock down at least 
9 3/8 bottles to earn enough points for the best prize. They see that they need to interpret this 
answer as at least 10 bottles in order to win the prize. 

The inequality properties of addition, subtraction, multiplication and division are given. When 
multiplying or dividing by a negative number, students are reminded about the reversal of the 
inequality sign. They also are reminded of how to translate phrases such as "at least" and "at 
most" to the appropriate relation in the Observations subsection. 

Common Student Errors 

• Students may have a hard time deciding which steps to follow to solve the inequality. They 
should connect this work back to the methods of solving linear equations. Students might 
make sign errors as they add or subtract from both sides of the inequality or reverse the 
inequality when multiplying or dividing by a negative number. 

• Students may have difficulty making the connection that C > means C is positive and C < 
means C is negative. 

• Although this section deals with the mechanical way of finding the solution set, students 
should be reminded that they should check to see if the solution set is reasonable. They need 
to keep using number sense. 

• Many students are able to find the answer using number sense without the written work. 
Learning how to write mathematics correctly is part of the communication skill and needs to 
be encouraged. This can cause frustration for students who find the problems easy to solve 
"in their heads." 

• Some students have difficulty remembering the meaning of the symbols, <, <, >, and >. They 
also have trouble translating the phrases such as "at least" and "at most." 



Topics in Algebra 1 ©2001 Texas Instruments Teacher Notes 4-17 



Chapter 4: Linear Inequalities 



Section 2: Using Algebra 




Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, or tell them to review the instructions on the worksheet. 

2. How to navigate the application, if they are not yet familiar with the application. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 

Observations 

The Observations give students an opportunity to practice finding the solution set to given 
inequalities. They are reminded about reversing the inequality sign when multiplying or dividing 
an inequality by a negative number. They also see a reminder of how to translate a phrase such 
as more than to the symbol >. 

If necessary, tell students how to find the Observations for this section. 



HRITE fln DBSERYHTinn . 



L'DL'.'E FDR :■:: 



-2X+3 i 11 

DH YDUR WORKSHEET 



Observation 1 

Solve for x: 
-2x+3<11 

x>~4. 

Students will see the answers on the next screen. Students' work 
may vary with the step order shown on the screen. 



L'DL'.'E FDR y: 



-i:.:-:: < ii EHSHHE 

t 
DID YDU REMEMBER TD 
CHARGE th* < t* > ? O 



Students label the result on a number line. A possible number 
line looks like this: 



-6 



-4 







Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-18 



Chapter 4: Linear Inequalities 



Section 2: Using Algebra 



Activities 



SELECT AA ACTIVITY 



5DLUEIT! 



PICK THE CORRECT 
STEPS Tn SOLVE 
THE EQUHTinn. 



SELECT £ PRESS [ERTER] O 



Scoring: Students get 
two attempts to solve 
each problem. They earn 
2 points for a correct 
answer on the first try, 1 
point for a correct answer 
on the second try. They 
get an additional 2 points 
for the correct solution. 

The total number of points 
available varies. 



Solve It! 

Tell students to: 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. Look at the algebraic expression at the top of the screen and 
decide what must be done to solve the inequality for x. 
Students must select from the choices offered; this activity 
presents only one sequence of steps (to first isolate x and then 
change the coefficient of x to 1), although other sequences may 
be correct. 

3. Press or to cycle through steps to choose from, and then 
press IENTERI to select the correct step (some problems require 
two steps). If their second choice is incorrect, the correct step 
is displayed; press any key to continue play. If the activity 
prompts them to select the correct result, highlight it with |T| 
or |T), and then press IENTERI to select it. As they play the 
activity, write each inequality and their strategy for finding the 
solution. 

4. Record the level they played. 

5. Record their scores. 



SELECT AA ACTIVITY 



FREEFRLLl 



UHRT GDES UP.. 
HUST CDHE DDUR 



SELECT £ PRESS [ERTER] O 



Scoring: Points are 
based on how quickly 
students solve each 
equation. If they give an 
incorrect answer, the 
equation stacks up at the 
bottom of the screen, 
giving them less time to 
solve the next equation. 

Unless you specify point 
or time limits for this 
activity, students can play 
the activity when four 
missed equations stack 
up, the game is over.or 
they press (QUIT) to stop. 
There is no time limit. 



Free Fall 

Tell students to: 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press IENTERI to select it. 

2. When they are ready to start, press any key. 

3. Watch the equation as it falls, and quickly solve for x. Enter the 
solution (press O for negative numbers), and press IENTERI 
before the equation hits bottom. If they give an incorrect 
answer, the correct answer is displayed; press any key to 
resume play. 

4. Follow your instructions. For example, students can play: 

• Until they have answered incorrectly four times (no time 
limit). 

• Until a certain amount of time has expired (highest score 
with the fewest misses wins). 

• Until a certain score has been reached (first student to 
reach the score with the fewest misses wins). 

• Repeatedly over a period of time (days, weeks, etc.) for 
tracking improvement of high scores. 

5. Record the level they played. 

6. Record their scores. 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-19 



Chapter 4: Linear Inequalities 



Section 2: Using Algebra 



Activities (continued) 

Additional Problems 

1. 6.4x > 16 when x>2.5 



1 
2. -x-2<-2 

2 



when x< 



3. 2x - 2.1 < -3.5 when x < -0.7 



4. Let C = the number of phone calls per month. Therefore, 15 + 0.25C < 30. The solution is 

C < 60. Students could discuss that this is about 2 calls per day. They should write whether or 
not this phone plan would be adequate for them. 



1 Try-It!™ on Your TI-83 Plus or TI-73 

This keystroke exercise lets students learn about the logic functionality built in the calculator. 
They see how to store a variable, test an inequality and finally graph a TRUE(1)/FALSE(0) graph. 
By graphing the solution set using the calculator's logic, they can verify their algebraic work on 
the inequalities. 

Students first solve the problem by hand. They should show all their work. 

If X=3, is 2X+4>7 true or false? 
Answer: 2(3) + 4 >7 

6 + 4 >7 
10>7 
Therefore, the statement is true. 

Tell students to follow the steps exactly on the calculators. Example screens are displayed on 
the worksheets for students to compare with the calculator screens. 

Additional Problems 

Tell students to do the following calculation by hand, and then check the answers using the 
calculator. They should show all their work. 



The graphs are shown below using ZDecimal flZOOMQ window values. Students should discuss 
how they determine the endpoint of the solution set. Remind them that using algebra gives the 
exact answer. The graph helps them see where the solution is approximately located. 



1. 



V2=fi.HK>ifi 



K=2.£ 



K>2.£ 



V=0 



2. 



V3=.£K-2J-2 


C 

.... 


.... 


K20 
K=0 


V=i 



3. 



VH=2K-2.K-3. 


£ 


- - - A 


n=-.r 


v=o 



Topics in Algebra 1 



©2001 Texas Instruments 



Teacher Notes 



4-20 



Chapter 5: Linear Systems 
Section 1 : Using Graphs & Tables 



Name 
Date 



Linear Systems: Using Graphs & Tables 




Student Worksheet 



Overview 



The Overview introduces topics covered in Observations and Activities. Scroll through the 
Overview using (TJ ( (TJ to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

The Observations illustrate that two lines in a plane intersect, are parallel or are the same line. 
By graphing the lines of a system of two linear equations with two variables, you can determine 
the possible number of solutions. Scroll through the Observations using UJ ( [JJ to review, if 
necessary). Read each screen carefully. When you come to a Write an Observation screen, stop 
and write the answer to the question on your worksheet. 



i.hdu Mflnv snmTinns 

DDES THIS SYSTEM OF 
LiriEHF; EOUflTinnS HAVE? 



USE VnUF; 
WORKSHEET! 



^ 




JX o 



Observation 1 

How many solutions does this system of linear equations have? 



2.HUU HfltlV SULUTIUnS 
DUES THIS SVSTEH OF 
LiriEHF; EOUflTinnS HAVE? 



USE YOUR 
UURHSHEET! 



A 



s 



Observation 2 

How many solutions does this system of linear equations have? 



3. HUM HflRV SULUTIURS 
DUES THIS SVSTEH UF 
LiriEHF; EOUflTIUnS Hli'.'E? 



USE YOUR 
UURHSHEET! 



*£ 



Observation 3 

How many solutions does this system of linear equations have? 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-1 



Chapter 5: Linear Systems 
Section 1 : Using Graphs & Tables 



Name 
Date 



Activities 

The Activities help you practice using graphs and tables. You can select from two different 
activities — System Match It! and a worksheet activity. Follow these steps to play the activities 
and complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or 0, and press I ENTER I . 





| SELECT AA ACTIVITY | 


■ 




Of 


SYSTEM HATCH IT! I 








l*|lttH.|fel 

[illilH D33IB 


SELE 


CT $. PRESS [EATER] 


O 



Scoring: You get one 

attempt to answer the 
problem. You earn 2 points 
for a correct answer. You can 
earn up to 12 points. 

Tip: Be careful! The graphs 
may appear close together. 





I SELECT AA ACTIVITY | 


X! 




Mr 


PLEASE SEE YDUR 
UDRHSHEET FDR 
HDRE ACTIVITIES. 








O 



Notes: See | Tip™ 4: 
Creating a Table to help you 
with tables. 

See also | Try-It!™ in 
Chapter 2 Sections 1 and 2 
for working with tables and 
linear equations. 



System Match It! 

1. Select the correct answer to the question. Questions include: 

• Selecting the graph that correctly illustrates the system. 

• Selecting the system that correctly describes a graph. 

• Selecting the correct solution of a system given a table. 

2. What was your score? 



Worksheet Activity 

Solve a system using tables. 

a. Blue Lake is Pat's favorite place to swim during the summer. 
There is an entry fee of $12.00 per car per day. Pat notices a sign 
as they approach the entrance. His family could join the Blue 
Lake Club for the summer! It costs $48.00 to join and then the 
entry fee becomes $6.00 per car per day. Fill in the table to help 
you develop the equations. 



Days at the 
Lake 


Cost Without 
Membership 


Cost With 
Membership 


1 


$12(1) = $12 


$48 + $6(1) = $54 


2 


$12(2) = $24 


$48 + $6(2) = $60 


3 






4 






• •• 


• •• 


• •• 


D 







b. Let C = the entry cost to the lake. Let D = the number of days 
Pat's family goes to the lake during one summer. Write the system 
of two equations that describe the cost of the entry fee without 
membership and with membership. Use the table above (in part 
a) to help you write the equations. 

Cost Without Membership: 

Cost With Membership: 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-2 



Chapter 5: Linear Systems Name 

Section 1 : Using Graphs & Tables Date 



Activities (continued) 



c. Check that the equations are written in slope-intercept form, 
y = rax + b. This prepares you to enter the system into your 
calculator. You will also have to change the variable. Notice that 
the cost, C, is the dependent variable (Y) and the number of days, 
D, is the independent variable (X). Write the equations so you can 
enter them in your calculator. 

Yl= 

Y2= 



d. Use a table to find the cost of the entry to the lake with and 

without membership. When is the entry cost without membership 
equal to the entry cost with membership? 



e. If Pat's family goes to the lake 6 times this summer, should they 
join the Blue Lake Club to save money? Why? 



If Pat's family goes to the lake 10 times this summer, should they 
join the Blue Lake Club to save money? Why? 



Challenge: Learn how to take a picture of a screen on your 
calculator using TI Connect™ software or TI-GRAPH LINK™ 
software and cable. You can paste a screen into a word processor 
and then print it out to hand in for your homework! Go to 
http://education.ti.com and search for TI Connect or 
TI-GRAPH LINK. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-3 



Chapter 5: Linear Systems 
Section 1 : Using Graphs & Tables 



Name 
Date 



1 Try-It!™ on Your TI-83 Plus or TI-73 

You will: 
• Graph two lines of a system of equations. 



• Use |TRACE| to locate the intersection of the lines. 

• Use 1 2nd| [TABLE] and |2nd| [TBLSET] to locate the exact solution of the system of equations. 

Find the solution of the system: Yl = -4X + 2 

Y2 = 2X - 2.5 

Notice that these equations are already in the form of y = mx + b. They are in the form to enter 
into your calculator. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. 


Exit the Topics in Algebra 1 
application and clear the Home 
screen. 


[2nd] [QUIT] 




(EXIT)ICLEARI 


2. 


First, enter -4X + 2 as Yl and 
2X - 2.5 as Y2 in the Y= editor. 

Note: See §Tlp™ 3: Graphing a Function in 
the Standard Window for more information. 

Note: On the TI-73, use \x\ rather than 
IX,T,0,nl. 










|Y=| ICLEARI 




M*ti M*t2 Plots 

W1B-4X+2 
\Y2B2X-2.5 
\Yj = 
\Vh = 
Ws = 




|(-)|4|X,T,e,/i|| + |2 


kl ICLEARI 
2|X,T,0,n|B2Q5 








3. 


Select the Zoom Decimal viewing 
window. The graph displays. 

Remember: You have to adjust the viewing 
window depending on the system of 
equations. You can see the intersection of 
the lines in the ZDecimal window for this 
example. 


TI-83 Plus: 










ofiWB MEMORV 
TTZBox 
2: Zoom In 
3: Zoom Out 
SBZDeciMal 
oTZS^iuare 
6:ZStandai-d 
7-i-ZTrig 




|Z00M| 4:ZDecimal 
TI-73: 


|Z00M| 8:ZDecimal 










\ 


f 




i 











Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-4 



Chapter 5: Linear Systems 
Section 1 : Using Graphs & Tables 



Name 
Date 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



To Do This 



Press 



Display (TI-83 Plus shown) 



4. Trace close to the intersection of 
the graphs to find a value close to 
the solution. 

Since Zoom Decimal traces by 
tenths, you can get close to the 
answer but this is not the exact 
answer. Notice that the point 
(0.8, "1.2) on the screen is on Yl. 
Is this point on Y2? Check it out! 

For this particular calculator 
setup, you don't get the exact 
answer. Read on to see how to 
refine the answer. 



ITRACEI 

H,H,H,orH 



V1=-HK+2 ] 




Use the table setup to refine the 
solution. 

Set up your table to show values 
close to X = 0.8. As shown here, 
you can use a starting value of 
with increments of 0.25. 



[2nd] [TBLSET] 

ICLEARI 0.25 |CLEAR| 



TABLE SETUP 

TblStart=0 

^Tbl=0.25 
Indpnt: KH1E Rsk 
Depend: ESEB Ask 



6. Search through the table to see 
that the lines intersect at (0.75, -1). 
Notice that both Yl and Y2 are -1 
when X = 0.75. Verify by hand that 
the solution is (X, Y) = (0.75, -1). 

You also know that there is only 
one solution because the lines 
intersect at one point, so your 
search is complete. 



2nd] [TABLE] 



X 


Vi 


V2 





2 


-2.E 


.25 


i 


-2 


lb— 



-i 


-i.£ 
-i 


i 


-2 


-.£ 


i.2£ 


"3 





IS 


-H 


.£ 


X=.75 



Note: Learn more about the calculator features intersect and Solver in the (§ Try-It!™ section in 
Chapter 5: Linear Systems, Section 2: Using Algebra. 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-5 



Chapter 5: Linear Systems Name 

Section 1 : Using Graphs & Tables Date 

Solution Search 

Write the solution and explain how you found the solution using graphs and a table for each of 
the problems below. Do the following for each problem. 

• Rewrite the system in slope-intercept form, y = mx + b, if necessary. 

• Use the slope-intercept form of the equations to draw a rough sketch of the lines. You can 
verify your graph on your calculator. Estimate the solution so that you have an idea of how 
many solutions there are and where the solution is located. 

• Search for the solution of the equation on the calculator using graphs and a table. 

• See If Tip™ 4: Creating a Table and (§ Tip 5: Adjusting the Viewing Window for additional 
help with the calculator. 

• Remember to change your viewing window ( IWINDOWI ) or your table setting ( |2nd| [TBLSET] ) 
to do your search. 

• Explain how you found the solution. 

• Write out how you checked the solution. 

Remember: The TI-73 and the TI-83 Plus only use the variables X and Y for graphs and tables. If an equation uses letters other than X and 
Y, you have to change the variables in the problem to X and Y on the TI-73 and the TI-83 Plus. Use parentheses, if needed, when entering 
the equations in the Y= editor. 

1. y = 2x + 4 
3x + y = -ll 



2. -x + 3y = 4 
1 10 

3 X + y = ¥ 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-6 



Chapter 5: Linear Systems Name 

Section 1 : Using Graphs & Tables Date 

Solution Search (continued) 

3. 2w + t = 35 

-2 1 
yw + ^19 



4. 4x + 7y = 8 

4x + 7y = 14 



5. x-9y = 7 
2x - 18y = 14 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-7 



Chapter 5: Linear Systems Section 1 : Using Graphs & Tables 



Linear Systems: Using Graphs & Tables Teacher Notes 

Objectives 

• To illustrate how to locate the real number solution of a system of linear equations (two 
equations and two variables) using tables. 

• To illustrate how to locate the real number solution of a system of linear equations (two 
equations and two variables) using graphs. 

• To graphically illustrate the types of solutions expected for a system of linear equations. 

Math Highlights 

Students work with a system of linear equations that has two equations in two variables. They 
begin the Overview by setting up an analysis of two different cell phone plans. The two plans 
can be modeled by linear equations. They investigate when the two plans cost the same amount 
of money. 

In the table of values example, students see a table of values for each equation. To create the 
table, the equations are in the form y = mx + b. They see that the x value that gives the same y 
value for both equations is the solution. They also see that they may need to refine the table of 
values to search for the solution. 

In the x-y graphical example, students graph both equations and locate the intersection of the 
lines. The (x,y) coordinate of the intersection of the lines is the solution. Since the graphs of the 
linear equations in the system can intersect, be parallel, or be the same line, students also see 
that they may find a unique solution, no solution, or an infinite number of solutions to the 

system. 

In Observations, students associate the graphs of the lines of a system with the number of 
solutions of the system. This is covered again at a higher level in Section 2: Using Algebra. 

Common Student Errors 

• Students have to rewrite the system in slope-intercept form in order to enter the equations 
into the calculator. Many students tend to make sign errors and division errors when they 
rewrite equations. For example, given 2T + 3S = 57 students would first have to rewrite the 
equation as S = (~2/3)T + (57/3), assuming S is the dependent variable. Then, the students 
have to rewrite this equation as Yl = (~2/3)X + (57/3). A common division error is to write 
the equation as Yl = (~2/3)X + 57, which is incorrect. 

• Students forget to enter fractions into the Y= editor using parentheses. Remind students 
about the order of operation. If they enter -2/3X, the calculator interprets this as -2 -=- (3 x X) 
following the order of operation rules. The correct entry is ("2/3) x X. 

Note: TI-73 users can use [jvfc] to enter the fractions. However, you should still remind them 
how to use parentheses and about the order of operation rules. 

• When solving by graphing using the graphing calculator, some students trace along one 
function to what appears to be the intersection point without verifying that that point is also 
on the other line. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Teacher Notes 5-8 



Chapter 5: Linear Systems Section 1 : Using Graphs & Tables 



Common Student Errors (continued) 

• After students have practiced using graphs and tables to solve a system of equations, they 
may think that they can always find the exact solution for a system using these methods. 
Although they can often find exact solutions using these methods, using algebra always 
gives exact answers for these equations. To help them understand this idea, have students 
try to search for the solution to the system y = 2x + 3 and y = 2x + 4. Using a table, they 
could search forever since these lines are parallel. Using a graph, they might think that the 
lines are parallel, but they are only looking at a few viewing windows. Ask them how they 
can know if there is a window where the lines intersect. Open a discussion with your class 
to see if they think they can verify that this system has no solution using tables or graphs. 

• Algebraic methods alone usually do not invite the student to reason out the solution using 
their knowledge of number sense and geometry. Many students learn the mechanics of 
solving a problem without understanding the problem or the solution. The graphs and tables 
method gives students the opportunity to see the values and graphs of the equations so they 
can see when two equations have the same value. 

Ask students to look at the equations y = 2x +3 and y = 2x + 4 again, and use their number 
sense. Ask them if 2x + 3 could ever be the same value as 2x + 4 for a given x? Encourage 
students to first look at the equations to see if their knowledge of geometry or their number 
sense can tell them something about the system before they start their method of solution. 

Some visual learners benefit by seeing the numbers and graphs first, and then by using these 
as the tool to find the solution. However, many students can see the solution to some 
systems using their number sense. These students may have difficulty taking the time to 
show and write about their work. This may also be an issue in Chapter 5: Linear Systems, 
Section 2: Using Algebra. Encourage student to use written mathematics as well as drawing 
graphs and tables as a communication tool. Have students look in newspapers and on the 
web for graphs and tables of information to show real examples for the need for this 
communication skill. 

Require students to write out complete solutions to problems, including the mathematics 
and the interpretation of what the numbers mean in the problem. For example, the cell 
phone problem in the Overview subsection requires not only the numeric answer but also an 
explanation about what the numbers mean with respect to the cell phone users. 



• 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Teacher Notes 5-9 



Chapter 5: Linear Systems 



Section 1 : Using Graphs & Tables 




Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, if necessary. 

2. How to navigate the application, if necessary. 

3. To scroll through the Overview on the calculator. Point out new terms, definitions, and 
concepts, and tell students to look for them as they go through the Overview. 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-10 



Chapter 5: Linear Systems 



Section 1 : Using Graphs & Tables 



Observations 

The Observations help students start to uncover the types of solutions that arise in systems of 
linear equations. If necessary, tell students how to find the Observations section. 

Students are asked to observe the number of solutions from the given graph. They should 
question whether they are seeing enough of the graph to make a conjecture about the number of 
solutions. 



Observation 1 



HRITE fln UBSERYRTIUn.. 



i.HDU Miinv suLUTiuns 

DDES THIS SYSTEM OF 
LiriEHF; EOUflTinnS HAVE? 



USE VnUF; 
UURHSHEET! 



^ 




JX o 



M.Ul'J.IH.IHJ.lT 

THE UUHBER DF SDLUTIDHS? 

i. i*f ; mw.iii«i.nim.iii 



HrmM*H| 



FflRflLLEL I * 



^ 



SflHELinESl 




■IX 



Students see the answer 
after the third observation 
question. 



Observation 2 



HRITE Rfl DRSERVRTinri.. 



2.HUU Mlin" SDLUTIDriS 
DUES THIS SVSTEH DF 
LiriEHF; EOUflTinriS Hli'.'E? 



USE YUUR 
UURHSHEET! 



A 



s 



M.Ul'J.IH.IHJ.lT 

THE UUHBER DF SULUTIUUS? 



INTERSECT 1 , \ 



I'flHE LiriEl'l 



K 



Observation 3 



HRITE Rfl URSERVRTIUR.. 



J. HUH Mlin" SDLUTIDriS 
DUES THIS SVSTEH UF 
LiriEHF; EQURTIDnS Hli'.'E? 



USE YUUR 
UURHSHEET! 



^ 



M,»,l'J,lll,l:m:lT 

THE UUHBER UF SULUTIUUS? 

s. nni<ft*^w:nTfn 



IRTERSECT | 



FflRflLLEL | 



BTJIEjBI I 



^ 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-11 



Chapter 5: Linear Systems 



Section 1 : Using Graphs & Tables 



Activities 





| SELECT Afl ACTIVITY | 


■ 




Of 


SYSTEM MATCH IT! I 








l*|lttH.|fel 

[illilH D33IB 


SELECT i. PRESS [ENTER] 


O 



Scoring: You get two 
attempts to answer the 
problem. You earn 2 points 
for a correct answer on the 
first try, 1 point for a correct 
answer on the second try. 
You can earn up to 12 points. 





| SELECT AA ACTIVITY | 


X! 




Mr 


PLEASE SEE YDUR 
UDRKSHEET FDR 
HDRE ACTIVITIES. 








O 



Notes: See | Tips™ 4: 
Creating a Table to help you 
with tables. 

See | Try-It!™ in Chapter 2 
Sections 1 and 2 for working 
with tables and linear 
equations. 



System Match It! 

Tell students to: 

1. Select the correct answer to the question. Questions include: 

• Selecting the graph that correctly illustrates the system. 

• Selecting the system that correctly describes a graph. 

• Selecting the correct solution of a system given a table. 

2. Record their scores. 

Remind students that the graphs might appear very close together 
on the screen. They need to use their knowledge about both the 
functions and the graph to determine the correct answer. 

Worksheet Activity 

Students investigate the entry fee to Blue Lake. They compare the 
entry fees with and without a membership fee. 

a. Students should gather information from the problem to write 
a system of equations for the investigation. Filling in the table 
with all of the calculations written out helps students develop 
the equations inductively. 



Days at the 
Lake 


Cost Without 
Membership 


Cost With Membership 


1 


$12(1) = $12 


$48 + $6(1) = $54 


2 


$12(2) = $24 


$48 + $6(2) = $60 


3 


$12(3) = $36 


$48 + $6(3) = $66 


4 


$12(4) = $48 


$48 + $6(2) = $72 








D 


12D 


48 + 6D 



b. Variables are suggested. Review the concept of independent 
and dependent variables with the students. 

Let C = the entry cost to the lake. 

Let D = the number of days Pat's family goes to the lake 

during one summer. 

C = 12D 

C = 6D + 48 (Students could also enter 48 + 6D.) 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-12 



Chapter 5: Linear Systems 



Section 1 : Using Graphs & Tables 



Activities (continued) 



c. Rewrite the problem in terms of Yl, Y2 and X to prepare to 
enter the system into the Y= editor. 



Yl = 12X 
Y2 = 6X + 48 



— or- 



Yl = 6X + 48 
Y2 = 12X 



Noti Not2 Plots 


W1B12X 


WzH6X+48 


Ws = 


Wh = 


We = 


Ws = 


W? = 



Enter equations in Y= editor. 



TRBLE SETUP 

TblStart=5 

^Tbl=l 
Indpnt: KH1E Rsk 
Depend: sSSSS. flsk 



Set up the table. 



K 


VI 


V2 1 


£ 


BO 


?B 


b 


72 


BH 


7 


BH 


90 


M^l 


9b 


9fi 


9 


10B 


102 


10 


ISO 


10B 


11 


132 


11H 


K(HJ =S 



The independent variable (days at the lake) and the dependent 
variable (entry cost) are stated in the problem. Remind 
students that the calculator treats X as the independent 
variable and Y as the dependent variable. 

d. Students need to enter the equations in the Y= editor and 
should set up the table. Discuss that the domain of the system 
should be whole numbers starting at since x counts the 
number of trips to the lake. Notice at x = 8, Yl = Y2 which is 
the breakeven point. If Pat's family goes to the lake up to and 
including 8 times, they might not choose to join the Blue Lake 
club. 

e. If Pat's family goes to the lake only 6 times during the summer, 
they will spend more money if they join the club for $48. 

f. If Pat's family goes to the lake 10 times during the summer, 
they will save money if they join the club. They will save 
$120 - $108 = $16. Discuss the savings if the family goes to the 
lake more than 10 times. Pose questions such as, when will 
they save $50? 

Have students find other situations that set fees in this manner. 
One source is the national and state park services web pages. 



Search for where the 
equations are equal. 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-13 



Chapter 5: Linear Systems Section 1 : Using Graphs & Tables 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Students search for the solution of a system of two linear equations in two variables using 
graphing and tracing, and a table. The problem has been chosen so that students do not trace to 
the exact solution and need to use the table to search. They could also choose to change the 
window so that they could trace to the exact solution. This is not an efficient choice, but could 
be pursued, and the investigation would be enriching. 

The students will: 

• Graph two lines of a system of equations. 

• Use |TRACE| to locate the intersection of the lines. 

• Use |2nd| [TBLSET] and |2nd| [TABLE] to locate the exact solution of the system of equations. 

Note: Students will learn more about the calculator features intersect (TI-83 Plus) and Solver (TI-83 Plus and TI-73) in the § Try-It! section 
in Chapter 5: Linear Systems, Section 2: Using Algebra. 

Tell students to follow the steps exactly on the calculators. Example screens are displayed on 
the worksheets for students to compare with the calculator screens. 

Solution Search 

Tell students to: 

• Rewrite the system in slope-intercept form, y = rax + b, if necessary. 

• Use the slope-intercept form of the equations to draw a rough sketch of the lines. Verify the 
graphs on the calculator. Estimate the solution so they have an idea of how many solutions 
there are and where the solution is located. 

• Search for the solution of the equation on the calculator using graphs and a table. 

Notes: Since the calculator only uses the variables X and Y for graphs, tables and some other features, students must decide which 
variable in the problem should be X and which one should be Y when the problem uses other variables. Discuss independent and 
dependent variables, emphasizing that the calculator is set up to treat X as the independent variable and Y as the dependent variable. 

Remind students to use parentheses correctly when they enter equations into the Y= editor. For example, (1/3)X is not the same as 
1/3X which is 1/(3X) when the order of operation rules are applied by the calculator. However, when TI-73 users enter 1/3 using the M\ 
key, their entry is calculated correctly. 

Remind students to change the viewing window ( IWINDOWI ) or table setting ( [2nd] [tblset] ) to do the search. § Tip™ 4: Creating a Table 
and i Tip 5: Adjusting the Viewing Window provide additional help with the calculator. 

• Explain how they found the solution. 

• Write out the check of their solution. 

Answers: 

1. (x, y) = (-3, -2) 

2. (x, y) = (3, 7/3) 

3. (w, t) = ("15, 65) Students are not given which variable is dependent and which is 
independent. They may very well write the solution as (t, w) = (65, "15). 

4. Lines are parallel, which implies that there are no solutions. 

5. Lines are the same, which implies that there are an infinite number of solutions. 

Topics in Algebra 1 ©2001, 2002 Texas Instruments Teacher Notes 5-14 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



Linear Systems: Using Algebra 




Student Worksheet 



Overview 



The Overview introduces the topics covered in Observations and Activities. Scroll through the 
Overview using [►] ( (T) to review, if necessary). Read each screen carefully. Look for new terms, 
definitions, and concepts. 

Observations 

Scroll through the Observations using [T] ( LTI to review, if necessary). Read each screen 
carefully. When you come to a Write an Observation screen, stop and write the answers to the 
questions on your worksheet. 

Observation 1 



m 


sun 




3flg 














HJliHHI.M HB9HHBM 
SAME sulutiur! 

SAME SYSTEM! 

DIFFERENT VARIABLES! ^ 



Find the solution of each system shown on the screen. Use either the 
substitution or elimination method. 



|i|ft««IJ.HHMKIiiim 



■2.\*v = 2 
■2.x*y - 5 



CAR "i :■:+:■' EQUAL 2iE 
FUR THE SAME <.^vY; 

USE YUUR UURKSHEET. 



Observation 2 

For the system of equations shown on the screen, can the expression 
~2x + y equal 2 and 5 for the same (x, y)? 



l!lft««IJ.HH«filiiim 
-2x+ V = 2 



SULYE USIRG ELIHIRATIUR. 
USE YUUR UURKSHEET. ^ 



Observation 3 

Solve the given system using the elimination method. 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-15 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



Activities 

The Activities help you practice using algebra to solve linear systems. You can select from two 
different activities — What Am I? and Balloon Ride. Follow these steps to play the activities and 
complete your worksheet. 

1. Make sure you are in the Activities for this section. 

2. Highlight an activity using or and press I ENTER I . 



s 



HHflT AH I? I 



CnnSISTEHT? 

DEPEHDEnT? 
iriDEFEriDEriT? 

incnnsisTEnT? 



SELECT i. PRESS [ENTER] O 



Scoring: You get one 

attempt to pick the correct 
classification of the system. 
You get 2 points for a correct 
choice and 1 point for a 
correct choice if you press 
(HINT) to see the graph. 

Four systems are given for a 
maximum score of 8 points. 



What Am I? 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press I ENTER I to select it. 

2. Look at the system of equations and decide if the system is 
consistent & independent, consistent & dependent, or 
inconsistent. 

Press (HINT) if you need to see the graph. You only get 1 point 
for the problem if you press (HINT). 

Press or to cycle through the choices and then press 
I ENTER | to select the correct answer. The correct answer and 
graph are displayed if the incorrect answer is chosen. You 
must press a key to continue play. 

3. In the space below, write out the algebraic steps (using 
elimination or substitution) for each problem or explain why 
you knew the correct answer. 



4. What level did you play? 

5. What was your score? 



Problem 1: 



Problem 2: 



Problem 3: 



Problem 4: 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-16 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



Activities (continued) 



gaEJBHBH 



BflLLDDR RIpTI 



SOLVE M SYSTEM ■ 
CLIME M HILL - 
THUE M RIDE! 



SELECT i. PRESS [ERTER] O 



Scoring: You get two 

attempts to pick or input the 
correct solution to the system 
of equations. You get 2 points 
for a correct choice or input 
on the first try, and 1 point for 
a correct choice or input on 
the second try. 

There are 4 problems for a 
maximum score of 8 points. 



Balloon Ride 

1. Highlight a level (silver = less difficult; gold = more difficult), 
and press I ENTER I to select it. 

2. Look at the system of equations and solve using the algebraic 
methods of substitution or elimination. 

Silver level: Press or to cycle through the solutions to 
choose from, and then press I ENTER I to select the solution. You 
must press a key to continue play. 

Gold level: Use or to select an answer or to get to the 
input box. Select or input your answer and press I ENTER I . 
(Press O to enter negative numbers.) You must press a key to 
continue play. 

3. As you play, write out the algebraic steps (using elimination 
or substitution) for each problem or explain why you knew 
the correct answer in the space below. 



4. What level did you play? 

5. What was your score? 



Problem 1: 



Problem 2: 



Problem 3: 



Problem 4: 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-17 



Chapter 5: Linear Systems Name 

Section 2: Using Algebra Date 

Extra Practice: Using Substitution or Elimination 

1. Cathy found a part-time job for the summer. Each week, when she works up to 10 hours, 
she earns a regular hourly wage. If she works more than 10 hours each week, she earns 
more money per hour for the overtime hours. She worked 14.5 hours during the first week. 
Her paycheck, before taxes and deductions, was $93.75. The second week, she worked 12 
hours and her paycheck, before taxes and deductions, was $75.00. Cathy's boss had told her 
what her hourly and overtime rates were, but Cathy was so excited to get the job that she 
couldn't remember what she was told. 

• Write a system of equations for Cathy's hourly and overtime pay rates. Clearly define the 
variables and their meanings. 



• Solve the system of equations using substitution. Show your work and explain the steps 
you used to solve the system of equations. Show the check of your solution. 



Write a sentence explaining Cathy's pay rate. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-1 8 



Chapter 5: Linear Systems Name 

Section 2: Using Algebra Date 



2. Cathy decides to spend some of her earnings from her new job, so she and her friend 
Brenda go to the mall. Their favorite store has blouses and jeans on sale. A variety of 
blouses is on one rack and are all the same price. A variety of jeans is on another rack and 
are all the same price. The price tags are not on the clothes but Cathy and Brenda know that 
the store's prices are usually within their budgets. 

Cathy picks out 3 blouses and 2 pairs of jeans from the sale racks. At the checkout, she sees 
that her total bill is $57.00. Brenda picks out 4 blouses and 3 pairs of jeans from the sale 
racks. Her total bill is $81.00. They are shopping in the state of Delaware where there is no 
sales tax. 

To find the cost of one blouse or one pair of jeans, Cathy and Brenda could just look at the 
sales receipt. Instead, they try to figure out the prices themselves. 

• Write the system of equations that Cathy and Brenda need to solve. Clearly define the 
variables and their meaning. 



Solve the system of equations using elimination. Show your work and explain the steps 
you used to solve the system of equations. Show the check of your solution. 

Hint: You can multiply both equations by a factor to avoid working with fractions! 



• Write a sentence explaining the price Cathy and Brenda paid for each top and each pair 
of jeans. 

Remember: You always have a choice of picking the method that you think will be easiest to perform when solving systems 
of equations. In the problems above, you are asked to use a specific method. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-1 9 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



| Try-It!™ on Your TI-83 Plus 

You will: 

• Graph two lines of a system of equations. 



• Use |TRACE| to locate the intersection of the lines. 

• Use the intersect feature to find the solution to a system of equations. 

• Check the solution on the home screen using |STO| . 



Find the solution of the system: 



Yl = -4X + 2 
Y2 = 2X -2.5 



Notice that these equations are already in the form of y = mx + b. They are in the form to enter 
into your calculator. 



To Do This 



Press 



Display 



1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 



[2nd] [QUIT] 
(EXIT) [CLEARl 



2. First, enter _ 4X + 2 as Yland 
2X - 2.5 as Y2in the Y= editor. 

Note: See §Tlp™ 3: Graphing a Function in the 
Standard Window for more information. 



[Y^I ICLEARI 
|Hl4 |X,T,e,n| f+1 2 
F1 ICLEARI 
2 |X,T,e,nl Fl2n5 



Noti 


Not2 


Plots 


WiB 


-4X+2 




WzH2X-2. 


5 


Ws = 






Wh = 






We = 






Ws = 






W? = 







Select the Zoom Decimal viewing 
window. 

Remember: You have to adjust the viewing window 
depending on the system of equations. You can see 
the intersection of the lines in the ZDecimal window 
for this example. 



[ZOOM] 4:ZDecimal 



MEMORY 
ox 

2: Zoom In 
3: Zoom Out 
SBZDeciMal 
STZS^uare 
6:ZStandard 
7-i-ZTrig 



4. The graph displays. Since this system 
has one solution, you can find the 
numerical solution using the intersect 
feature. 

Important Reminder: Be sure to use your 
knowledge about the equations of lines to determine 
if the lines are parallel or the same line. When you 
use the intersect feature, an error displays if the lines 
are parallel. If the lines are the same line, the 
calculator shows ONLY one answer. 



] 


f 


i 





Use the CALCULATE menu item 
called intersect to find the calculated 
numeric solution. 



[2nd] [CALC] 5:intersect 



SiHMlIiUa 



l:ualue 
2: zero 
3:MiniMUM 
4: Max i mum 
sfl intersect 
6:dy/dx 
7:XfCx>dx 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-20 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



To Do This 



Press 



Display 



6. You have to select a First Curve in 
order for the calculator to calculate 
the numerical solution. Notice the 
cursor is on the line Yl = ~4X + 2. 



I ENTER] 



V1=-HK+2 ] 




You have to select a Second Curve in 
order for the calculator to calculate 
the solution. Notice the cursor is on 
the line Y2 = 2X - 2.5. 



ENTER 



V2=2K-2.£ ] 




Second curve? 
K=.9 dV=-.7 



The calculator now needs a close 
guess at the solution. Move the 
cursor closer to the intersection. 



H or [T| 



V2=2K-2.£ ] 




Guess? 

K=.B j1V=".9 



The calculator uses a program to 
calculate the numerical solution. The 
numerical solution given is at 
(0.75, -1). Check to see if this 
solution is the exact solution or an 
approximate value. 



ENTER 




Intersection 
K=.7£ ^V=-i 



10. Check the solution on the home 

screen. The value 0.75 is stored in the 
X variable in the calculator. X is fixed 
at 0.75 after you follow these steps. 

Important Reminder: The calculator always has a 
value stored in each variable. You must store the 
value you want in order to understand how the 
calculator interprets a variable expression. 



[2nd] [QUIT] ICLEARI 
□ 75 

[s7o»1[x7ne^1lENTERi 




11. Enter -4X + 2 to find the Yl value at 
X = 0.75. Notice that the output is "1. 



O 4 |X,T,e,n| [+1 2 | ENTER I 




12. Enter 2X - 2.5 to find the Y2 value at 
X = 0.75. Notice that the output is ~1 
and Yl = Y2 at X = 0.75. 

The solution is (0.75, -1). Press 
IGRAPHI to see if this agrees with 
the graph of the lines! 



2 |X.T.e,nl Fl2n5 
I ENTER I 



.75*X 
-4X+2 
2X-2.5 



,75 
-1 
-1 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-21 



Chapter 5: Linear Systems Name 

Section 2: Using Algebra Date 

Extra Practice: Using Your Calculator to Find Solutions 

1. Use your calculator to find the solution to each system of equations. Write the solution and a 
description of how you used your calculator to find and verify the solution. 

Remember: You need to rewrite the equations in the form y = mx + b to work with your calculator. 

2 
Note: If the calculator gives the value .6666666667 or X- 66666666666666 in Solver the exact answer is most likely X = - . 

Explain how you found the exact answer if the calculator only gave an approximate answer. Verify your answer! 



a. y = -1.2x + 3.725 b. 3x + y = 6 

3x - y = 8.875 |x - |y = "1 



2. Solve each of the systems you found in Extra Practice: Using Substitution or Elimination, 
using your calculator. Write an explanation of how you used your calculator. 

a. Cathy's pay rate 



b. Cathy and Brenda's shopping trip 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-22 



Chapter 5: Linear Systems Name 

Section 2: Using Algebra Date 



Challenge 

Investigate using the Solver feature on the TI-83 Plus to find the solution! Find this feature in 
I MATH I 0:Solver. It is best to use this feature if the system has only one solution . 

Hint: Press I math I and select 0:Solver.You have to enter the equation in the Solver as = - 4X + 2 - (2X-2.5) to solve for the X value. You 
have to input a guess for the X solution, bound = {-1E99, 1E99} represents the real number line for the calculator. You can make the set 
smaller to find solutions in a particular interval. Then, use lALPHAI [solve] to find the calculator's numerical solution. See the TI-83 Plus 
guidebook for more details about the Solver feature. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-23 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



1 Try-It!™ on Your TI-73 

You will: 

• Graph two lines of a system of equations. 

• If the lines intersect, use the I MATH I feature Solver to find the X value of the solution to the 
system. 

• Find the Y value by using |ST0»| on the home screen. 

Find the solution of the system: Yl = ~4X + 2 

Y2 = 2X - 2.5 



Notice that these equations are already in the form of y = mx + b. They are in the form to enter 
into your calculator. 



To Do This 



Press 



Display 



1. Exit the Topics in Algebra 1 
application and clear the Home 
screen. 



[2nd] [QUIT] 
(EXIT) [CLEARl 



2. It is good practice to look at the 
graph of the system before you use 
the Solver feature. Enter -4X + 2 as 
Yl and 2X - 2.5 as Y2 in the 
Y= editor. 

Note: See g Tip™ 3: Graphing a Function in the 
Standard Window for more information. 



|Y=| ICLEARl 



Q 4 \x\ {+} 2 
R ICLEARl 
20B2Q5 



Noti 


Not2 Plots 


WiB 


-4X+2 


WzH2X-2.5 


Ws = 




Wh = 





3. Select the Zoom Decimal viewing 
window. 

Remember: You will have to adjust the viewing 
window depending on the system of equations. You 
can see the intersection of the lines in the ZDecimal 
window for this example. 



[ZOOM] 8:ZDecimal 



BtMBB MEMORY 
2TZo 



oom In 
Zoom Out 
ZQuadrantl 
ZS^iuare 
ZStandard 
ZoonStat 



ajZDeoinal 



4. The graph displays. Since this system 
has one solution, find the numerical 
solution next using the Solver 
feature on the TI-73. 

Important Reminder: Before you use the intersect 
feature, use your knowledge about the equations of 
lines to determine if the lines are parallel or the same 
line. 



] 


/ 


; 





5. 



Use the I MATH I menu item called 
Solver to find the calculated 
numerical solution. 



[MATHl 6:Solver 



BiaiZ HUM PRB LOG 

2:godC 

3:3 

4:3J"< 

aJSoluer... 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-24 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



To Do This 


Press 


Display 


6. To find the solution, you want to find 
when the two equations are equal. 
Find Yl = Y2. You need to enter 
-4X + 2 = 2x - 2.5 on the eqn: line. 


B40E2 










EQUATION SOLUER 
e-=in: "4X+2 










7. Find the equal sign (=) in [2nd] [text]. 


[2nd! [TEXT] 










HBCDEFGHIJ 
H L H n n P Q F; 1" T 
M '! M K V 2 i J " _ 

= ^ > > < < and ok 




\zl\zl\zl |ENTER| 



IDonel 


= 








8. Finish entering the equation. 










|ENTER|2[xJbJ2U5 




EQUATION SOLUER 
e°in: "4X+2=2X-2.5 










9. Enter a guess of X=l as the solution. 
The calculator needs a starting value 
for its computation. 

Hint: bound = {-1E99, 1E99} represents the real 
number line for the calculator. You can make the set 
smaller to find solutions in a particular interval. See 
the TI-73 guidebook for more details. 










IENTERI ICLEARI 1 




-4X+2=2X-2.5 
X=l 

bound=C-lE99 ? l... 
SolueiX 










10. Highlight X on the Solve:X line and 
the solution is given as iX=.75. 
Notice that ■ appears after the 
calculator has computed the 
numerical solution. 










\zl H |ENTER| 




-4X+2=2X-2.5 
■X=.75 

bounds -1e99,1... 

SolueiX 










11. Find the Yl and Y2 values on the 
home screen using |STO|. The value 
0.75 will be stored in the X variable 
in the calculator. X is fixed at 0.75 
once you follow these steps. 

Important Reminder: The calculator always has 
some value stored in each variable. You must store 
the value you want in order to understand how the 
calculator interprets a variable expression. 










|2nd| IQUITI ICLEARI 

□ 75 




. 75*X . 75 




ISTOI |x| IENTERI 








12. Enter -4X + 2 to find the Yl value. 
Notice that the output is "1. 










IHI4UM + I 2 IENTERI 




. 75*X . 75 
-4X+2 -1 











Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-25 



Chapter 5: Linear Systems 
Section 2: Using Algebra 



Name 
Date 



To Do This 


Press 


Display 


13. Enter 2X - 2.5 to find the Y2 value. 
Notice that the output is -1 and 

Yl = Y2atX = 0.75. 

The solution is (0.75, *1). Press 
|GRAPH| to see if this agrees with the 
graph of the lines! 












2[xJbJ2|J5|ENTER| 




.75*X 
-4X+2 
2X-2.5 


.75 
-1 
-1 













Extra Practice: Using Your Calculator to Find Solutions 

1. Use your calculator to find the solution to each system of equations. Write the solution and a 
description of how you used your calculator to find and verify the solution. 

Remember: You need to rewrite the equations in the form y = rax + b to work with your 
calculator. 

2 
Note: If the calculator gives the value .6666666667 or X- 66666666666666 in Solver, the exact answer is most likely X = - . 

Explain how you found the exact answer if the calculator only gave an approximate answer. Verify your answer! 



a. y = -1.2x + 3.725 
3x - y = 8.875 



b. 3x + y = 6 
1 1 . 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Student Worksheet 5-26 



Chapter 5: Linear Systems Name 

Section 2: Using Algebra Date 



2. Solve each of the systems you found in Extra Practice: Using Substitution or Elimination 
using your calculator. Write an explanation of how you used your calculator. 



a. Cathy's pay rate 



b. Cathy and Brenda's shopping trip 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Student Worksheet 5-27 



Chapter 5: Linear Systems Section 2: Using Algebra 



Linear Systems: Using Algebra Teacher Notes 

Objectives 

• To review the substitution method of solving a system of two linear equations in two 
variables. 

• To review the elimination method of solving a system of two linear equations in two 
variables. 

• To review the definitions of consistent (independent and dependent) and inconsistent 

systems. 

• To associate the number of solutions of a system with the classification of consistent 
(independent and dependent) and inconsistent systems. 

Math Highlights 

In this section, students work with a linear system of equations with two equations and two 
variables and review the methods of substitution and elimination. 

In the Overview, students associate the graphs of the lines of a system with the number of 
solutions of the system and the classification of the system as consistent and inconsistent 
(dependent and independent) systems. This was also covered at a lower level in 
Section 1: Using Graphs & Tables. 

In the substitution example, caramel corn is sold as a class fundraiser, and the students need to 
know how many bags of caramel corn they need to sell to make a profit. A system of linear 
equations is written to model the costs of producing the caramel corn and the revenue earned 
from selling bags of caramel corn. Solving the system of equations gives the number of bags of 
caramel corn the students need to sell to make a profit. The term profit is used and should be 
discussed in the class. The terms breakeven and loss are not covered, but students would benefit 
from a complete classroom discussion of the problem, not just the profit point. 

In the elimination example, Jon and Mia earn money by recycling cans and glass. The recycling 
center gives each of them one payment for both the cans and the glass. Jon and Mia want to 
know how much money they earned for each pound of cans and each pound of glass. A system 
of linear equations is written to model the amount of money that Jon and Mia earned for 
recycling. Solving the system of equations gives the prices per pound that they were paid for 
cans and glass. Students can eliminate either variable in the example. 

The variables used in these problems are x and y; however, you should encourage students to 
use variables that make sense in the problem. 

The (D Try-It!™ examples for the TI-83 Plus and the TI-73 are slightly different. They are printed 
on separate pages so that you can make copies of only the pages you need. Students can use 
either calculator to complete the problems in the Student Worksheet. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Teacher Notes 5-28 



Chapter 5: Linear Systems Section 2: Using Algebra 



Common Student Errors 

• When they use the substitution method, students may make sign and division errors when 
they solve for one of the variables. They may also need to be reminded to use parentheses 
when needed. Students might incorrectly distribute expressions. 

• When solving by substitution, students might solve one equation for y (or x) and substitute 
back into the same equation getting a result of = 0, when they should have substituted 
back into the other equation. 

• When they use the elimination method, students may miss multiplying every term in an 
equation by the appropriate constant. 

• As they continue using the elimination method, many students subtract incorrectly. They 
usually subtract the first term correctly, but often forget to subtract the other terms. 
Encourage students to choose the multiplier so that they add the equations for the 
elimination rather than subtract them. 

• When an algebraic solution results in a statement that is always true, such as 2 = 2 in a 
dependent system (coincident lines), or a statement that is never true, such as 2 = 4 in an 
inconsistent system (parallel lines), students may be unsure how to state the solution. 

• Students often skip checking their solution. In addition to checking their solution by 
substituting it back into the original equations, they should also make sure that the solution 
is reasonable. For example, in the Student Worksheet problem where Cathy and Brenda are 
shopping for tops and jeans, the variable must be positive. 

• Students should practice rewriting the system after each step to keep track of their 
manipulations. 

Encourage students to create good math habits by doing the following. 

• Pick the method — graphs, tables, substitution, or elimination — which is best for the system. 
First, look at the physical problem, if appropriate, or use geometry and number sense to 
analyze the system. 

• Remember that for real problems (word problems), some solutions may need to be omitted. 
For example, if you need to find the quantity of an item, the solution must be positive. 

• Notice when a system obviously has no solution because the lines have the same slope 
(i.e., parallel lines), and when a system has an infinite number of solutions because the lines 
are the same line. 

• Rewrite the system after each step to keep track of the manipulations. 

Note: Students who can think through the steps in their mind tend to be impatient with recording each step. However, forming this habit 
now will help them in the future, especially when they learn how to solve systems using matrices. 

• Write out the mathematics you use to solve the system. Also, write phrases or sentences that 
explain your steps. Draw graphs and tables to use as aids. 

• Interpret what the solution means in real problems. For example, the recycling problem in 
the Overview subsection requires not only the numeric answer but also an explanation about 
what the numbers mean with respect to the price per pound. 

Tip: Have students look in newspapers and on the web for graphs and tables of information to show real examples of the importance of 
both computations and explaining what the computations mean. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Teacher Notes 5-29 



Chapter 5: Linear Systems 



Section 2: Using Algebra 



Student Worksheet Notes with Answers 
Overview 

Tell students: 

1. How to find the Overview, if necessary. 

2. How to navigate the application, if necessary. 




3. To scroll through the Overview on the calculator. Point out new terms, definitions, 
and concepts, and tell students to look for them as they go through the Overview. 



Observations 

The Observations help students review substitution and elimination methods. If necessary, tell 
students how to find the Observations. 



l!l»H«1il,l:m:VJ:«ni^ 



FiriD THE SDLUTIDH 
nF EACH SYSTEM. 



USE VnUF; UDRKSHEET. 



Observation 1 

Students are asked to solve both systems using either the 
substitution method or the elimination method. The systems are 
identical except for the choice of variables. Students should become 
comfortable with a change in variables and should recognize that 
they do not have to do this calculation twice. 



■*P!FP 


sun 




3flg 














HJliHHI.M HB9HHBM 

SANE SDLUTIDH! 

SAME SYSTEM! 

DIFFERENT VARIABLES! ^ 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-30 



Chapter 5: Linear Systems 



Section 2: Using Algebra 



Observations (continued) 



URITE Mil DESEfi'.'MTinri 



■2x*<> ■■ 
■j.x*v ■■ 



CAR "i :■:+:■' EQUAL UE 
FuR THE SAME (Xjyl? 

USE VnUF; UnRKSHEET. 



Observation 2 

Students are asked if the same left-hand sides of the equations can 
equal different right-hand sides. They should be able to reason this 
out using their number sense. They can then verify their answer 
using algebra. They will see the verification using the elimination 
method on the following screens in the application. 

The second equation is multiplied by _ 1 and then the equations are 
added. Multiplying by -1 was chosen to avoid sign errors. 

Some students will want to immediately subtract the two equations. 
This is also correct, but they need to be very careful to subtract each 
term! 





■Zx*y = 2 

0=-3H3E3 




THERE IS AD SDLUTinn! 




HiU.httUUiU 












| URITE AM nBSERYRTinn | 


Observation 3 


"2x+ V - 2 
■Hx+2v = H 


Students see the elii 


SuLYE USImG ELIHImhTIDm. 
USE YDUR HuRKSHEET. fy. 


application. The res 














| URITE RR nRSERYATinn | 




Hx-2v ="H 
-HX+2V = H 

o = orrarra 




SAKE LIRE! ARY RDIRT DR 
-Hx+2v = H IS A SnLUTinR! 




MilfetHHM&IMHMMMQ 







Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-31 



Chapter 5: Linear Systems 



Section 2: Using Algebra 



Activities 





1 SELECT fln ACTIVITY | 


■ 






HHflT MM I? | 




cnnsisTEnT? 

DEPEtlDEriT? 

inDEPEnDEriT? 
incnnsisTEnT? 




SELE 


ICT i. PRESS [ENTER] 


o 



Scoring: Students get one 
attempt to pick the correct 
classification of the system. 
They earn 2 points for each 
correct choice, and 1 point 
for a correct choice if they 
press (HINT) to see the 
graph. 

Four systems are given for a 
maximum score of 8 points. 



What Am I? 

Tell students to: 

1. Highlight a level (silver = less difficult; form y = rax + b; gold = 
more difficult; mixed slope-intercept and standard forms), and 
press I ENTER I to select it. 



2. 



3. 



4. 



Look at the system of equations and decide if the system is 
consistent & independent, consistent & dependent, or 
inconsistent. 

Write out the algebraic steps to make this determination, except 
possibly at the silver level. Students could use their knowledge 
of the graph of y = rax + b in order to answer some problems. 

Press (HINT) if they want to see a graph of the system. They will 
only get 1 point for the problem if they use the (HINT). 



5. Press or to cycle through the choices and then press I ENTER I 
to select the correct answer. The correct answer and graph will 
show if the incorrect answer is chosen. They must press a key to 
continue play. As they play the activity, students should write an 
algebraic solution to the system on their worksheet. 

6. Record the level they played. 

7. Record their scores. 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-32 



Chapter 5: Linear Systems 



Section 2: Using Algebra 



Activities (continued) 



SELECT fln ACTIVITY 



BflLLDDR F;IDE~| 



SOLVE A SYSTEM ■ 
CLIMB A HILL - 
TAKE H RIDE! 



SELECT $. PRESS [EATER] O 



Scoring: Students get two 
attempts to pick or input the 
correct solution to the system 
of equations. They earn 2 
points for a correct choice or 
input on the first try, and 1 
point for a correct choice or 
input on the second try. 

There are 4 problems for a 
maximum score of 8 points. 



Balloon Ride 

Tell students to: 

1. Read the introduction screen and then highlight a level (silver = 
less difficult; gold = more difficult), and press I ENTER I to select it. 
Students answer multiple-choice problems in the silver level and 
they input their solution in the gold level. 

Silver Level: Press or to cycle through the solutions to 
choose from, and then press I ENTER I to select the solution. 
Students must press a key to continue play. 

Gold Level: Use or to select an answer or to get to the 
input box. Select or input your answer and press I ENTER I . (Press 
to enter negative numbers.) Students must press a key to 
continue play. 

3. As they play the activity, students should write their work using 
either elimination or substitution. 



4. Record the level they played. 

5. Record their scores. 

Extra Practice: Using Substitution or Elimination 

1. Cathy's pay rate can be determined by the following. 

Let S = hourly pay rate 
Let T = overtime pay rate 

Weekl: 10S + 4.5T = 93.75 

Week 2: 10S + 2T = 75 -> 10S = 75-2T 

To use substitution, the student could solve the Week 2 equation for 10S, 10S = 75-2T. Then, 
the Week 1 equation becomes the following. 

(75 - 2T) + 4.5T = 93.75 -> 2.5T = 18.75 -> T = 7.5 

Once T is known, substitute T into either equation and solve for S. 

10S + 4.5(7.5) = 93.75 -> 10S = 60 -> S = 6 

Interpret the answer: 

S = $6.00 per hour 
T = $7.50 per hour 

Cathy earns $6.00 per hour for the first 10 hours and $7.50 per hour for any overtime. 



Topics in Algebra 1 



© 2001 , 2002 Texas Instruments 



Teacher Notes 



5-33 



Chapter 5: Linear Systems Section 2: Using Algebra 



2. Brenda and Cathy can figure out the cost of each top and pair of jeans purchased by the 
following. 

Let T = price of one top 

Let J = price of one pair of jeans 

Cathy: 3T + 2J = 57 

Brenda: 4T + 3J = 81 

To use elimination, multiply Cathy's equation by 4 and Brenda's equation by "3. 

Cathy: 12T + 8J = 228 

Brenda: -12T - 9 J = "243 

Add the two equations to get: 

-J = -15 -> J = 15 

Substitute this value for J into either equation to find T. 

3T + 2(15) = 57 -> 3T = 27 -> T = 9 

Interpret the answer: 

T = $9.00 per top 

J = $15.00 per pair of jeans 

Cathy and Brenda paid $9.00 for each top and $15.00 for each pair of jeans. 

1 Try-It!™ on Your TI-83 Plus and TI-73 

Note: The § Try-It! exercises cover different functionality available to solve a system of equations. The TI-83 Plus exercise uses the 
intersect feature that the TI-73 does not have. The TI-73 exercise uses the Solver to solve an independent system. The TI-83 Plus also has 
a Solver feature. Using the Solver feature on the TI-83 Plus is given as a challenge investigation for the students. (Hints are given below.) 
The linear system to be solved is the same for both calculators. The problem set, Using Your Calculator to Find Solutions, given after the 
i Try-It!, is identical and is repeated after each § Try-It! for your copying convenience. 

On the TI-83 Plus, students will: 

• Graph two lines of a system of equations. 

• Use |TRACE| to locate the intersection of the lines. 

• Use the [2nd] [CALC] intersect feature to find the solution to a system of equations. 

Check the solution on the home screen using |ST0»| . 

On the TI-73, students will: 

• Graph two lines of a system of equations. 

• If the lines intersect, use the I MATH I Solver feature to find the X value of the solution to the 
system. 



• Find the Y value by using the |ST0»| on the home screen. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Teacher Notes 5-34 



Chapter 5: Linear Systems Section 2: Using Algebra 

Reminders for the § Try-It!™ Exercises 

TI-83 Plus and TI-73: 

• Only the variables X and Y are used for graphs and tables. If an equation uses letters other 
than X and Y, you have to change the variables in the problem to X and Y in order to use 
some features on the calculators. 

• Some value is always stored in each variable. You must store the value you want in order to 
understand how the calculator interprets a variable expression. The calculator does not 
perform symbolic manipulations. 

• The intersect feature on the TI-83 Plus and the Solver feature on both the TI-83 Plus and the 
TI-73 are best used to find the solution to a system with one solution. Students should use 
their knowledge about the equations of lines to determine if lines are parallel or the same 
line before working the problem. 

• In the Solver, bound = {-1E99, 1E99} represents the real number line for the calculator. You 
can make the set smaller to find solutions in a particular interval. See the TI-83 Plus or TI-73 
guidebook for more details. 

TI-83 Plus: 



• 



When the intersect feature is used, an error is displayed if the lines are parallel. If the lines 
are the same line, the calculator will show only one answer. 

• In the challenge problem, students are asked to investigate using the Solver feature on the 
TI-83 Plus to find the solution. Find this feature in [MaTHI 0:Solver. See the TI-83 Plus 
guidebook for details about the Solver feature. You have to enter the equation in the Solver 
as = _ 4x + 2 - (2x - 2.5). You have to input a guess for the X solution. Then, use IALPHAI 
[SOLVE] to find the calculator's numerical solution. 

Extra Practice: Using Your Calculator to Find Solutions 

Note: These problems are identical for both the TI-83 Plus and the TI-73. 
la. (3,0.125) 

lb. (2/3,4) 

2a. Answers will vary. Students use their choice of calculator feature to solve for Cathy's pay 
rate. 

2b. Answers will vary. Students use their choice of calculator feature to solve for Cathy and 
Brenda's shopping trip. 



Topics in Algebra 1 © 2001 , 2002 Texas Instruments Teacher Notes 5-35 



|| Tip 1 : Resetting Your Calculator 



Tip™ 1 : Resetting Your Calculator 




You can easily reset all default, or factory, settings on your calculator from the MEMORY menu. 
Resetting the default settings ensures that all calculators show exactly the same results in the 
same form. 

Resetting defaults does not erase any lists, programs, or variables stored in memory. 

Note: You should reset your calculator's default settings to ensure that the results you see on your calculator will match the results in all 
example screens in the 1 Tips. 



Resetting your calculator to the defaults 


For more information 


Resets all mode and window format defaults. 


H Tip 2: Adjusting Your Calculator Settings 


Turns off function plots. 


H Tip 3: Graphing a Function in the Standard Window 


Resets window values to ZStandard. 


(§ Tip 5: Adjusting the Viewing Window 


Turns off statistical plots. 


(§ Tip 7: Creating a Statistical Plot 



Calculator Keys Used in This i Tip™ 

[2nd] [MEM] 7:Reset 2:Defaults 2:Reset 

1 Tip™ Highlights 

Your calculator contains many settings that control the interpretation of results and graphs. For 
example, you can control how the calculator: 

• Displays mathematical results (for example, with floating or fixed decimal notation). 

• Interprets and displays graphs and statistical plots (for example, scale of the X-axis and 
Y-axis). 

Note: Types of settings vary between the TI-83 Plus and the TI-73. For more information, see the calculator guidebook. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 1-1 



|| Tip 1 : Resetting Your Calculator 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Reset the calculator defaults. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Display the MEMORY menu and 
select Reset. 


[2nd] [MEM] 
7: Reset 










iMMflfl 




1 : Rbout 

2: Men Mgnt/Del... 

3: Clear Entries 

4:ClrRllLists 

5:Rrchiue 

6:UnRrchiue 

OJReset... 








2. Select Defaults. 


2:Defaults 










ssn rrchiue rll 

^Defaults... 




3. Select Reset to reset the calculator. 


2: Reset 










atfdaHddttfflUMe 




fflReset 


4. Clear the screen and return to the 
Home screen. 












TI-BSNus 
1.12 

Defaults set 




ICLEARI 




TI-83 Plus 






GRAPH EHFLnFiEF; SOFTWARE 
i.HO 

Defaults set 






TI-73 





You are now ready to work through the (§) Tips. Remember, resetting the calculator ensures that 
you get the same results shown in all (j§ Tips examples. 

After you become familiar with your calculator, it will not be necessary to reset it every time 
because you will know how you have changed the settings, and you will understand the results 
the calculator displays in light of those changes. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 1-2 



§ Tip 2: Adjusting Your Calculator Settings 




Tip™ 2: Adjusting Your Calculator Settings 



You can control how the calculator displays results and graphs by changing settings. For 
example, the mode settings screen is displayed below (varies slightly for the TI-73). The 
highlighted settings are the ones that are selected. 



All highlighted 
settings are selected. 




>e-=iuent.ia 

:eal 

ull 



Sci En9 
0123456789 

Degree 
ar Pol Se-=i 
Dot 
II Sinul 
a+bi re^ei 
Horiz G-T 



Calculator Keys Used in This i Tip™ 

• [MODE] 

• [2nd] [FORMAT] 

1 Tip™ Highlights 

This (D Tip shows how to change settings on two frequently-used screens — the mode screen and 
the window format screen. For more information about settings, see the calculator guidebook. 



• Mode ( IMODED settings determine how the calculator interprets and/or displays numbers and 
results. 

• Window format (" 1 2nd I [FORMAT]) settings determine how the calculator interprets and/or 
displays graphs. 

Note: The TI-83 Plus and the TI-73 mode and window format screens are slightly different. 



TI-83 Plus 



TI-73 



Sci En9 
0123456789 

De9ree 
ar Pol Se^i 
" Dot 
I Sinul 

Horiz G-T 




Mode screen 




PolarGC 
CoordOff 
GridOn 

RxesOff 
Label On 
xprOff 



Window Format Screen 




Sci 
0123456789 

Radian 
b^c 

Mans i mp 




CoordOff 
GridOn 
RxesOff 
Label On 
xprOff 



Mode screen 



Window Format Screen 



In the d) Try-It! example, you will select new calculator settings following these main steps. 

1. Display the setting screen. 

2. Press EL EL EL or EL as necessary, to highlight the setting you want to select. 



3. Press IENTERI to select it. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 2-1 



§ Tip 2: Adjusting Your Calculator Settings 



1 Try-It!™ on Your TI-83 Plus or TI-73 
Change a Mode Setting 

Change the mode setting so that results display to 2 decimal places. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Display the mode settings screen. 

Note: The TI-73 mode screen varies slightly from 
the TI-83 Plus. 



[MODE] 



Sci En9 
0123456789 

De9ree 
ar Pol Se^i 
Dot 
I Sinul 

Horiz G-T 




2. Change the decimal notation setting 
from Float to 2. 



until Float is 
highlighted 
UJ until 2 is 
highlighted 
IENTERI to select 



!MUuHI boi En9 



\oai_e 1^3456739 
De9ree 
ar Pol Se^i 
""" Dot 
] Sinul 




Horiz G-T 



3. Press [2nd] [QUIT] to return to the 
Home screen, and clear the current 
line, if needed. 

Tip: Pressing [2nd] [Quit] always takes you back to 
the Home screen, except in the Topics in 
Algebra 1 application. 



2nd] [QUIT] 



ICLEARI 



4. Calculate 1.479 + 2.897. 



1Q479B 
2Q897 



ENTER 



1.479+2.897 



4.38 



The calculator 
rounds the result to 
2 decimal places. 



5. Change the decimal notation setting 
back to Float. 

Note: Float displays a number up to 10 digits. 



[MODE] 

until Float is 

highlighted 

IENTERI to select 



Sci En9 
0123456789 

Degree 
ar Pol Se^i 
Dot 

J Sinul 
i. re-^ei. 
Horiz G-T 




6. Return to the Home screen. 



2nd] [QUIT] 



7. Calculate 1.479 + 2.897 again. 

Tip: On the TI-73, you can press H H to 
highlight a previous entry on the Home screen, 
and then press Ienteri to paste it to the current 
line. 



[2nd] [ENTRY] to display 
the previous entry 

IENTERI 



1.479+2.897 
1.479+2.897 



4.38 
4.376 



The calculator 

displays up to 10 — 

digits. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 2-2 



§ Tip 2: Adjusting Your Calculator Settings 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Change a Window Format Setting 

To display a grid on the graph screen, select GridOn from the window format screen. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Display the window format screen. 

Note: The TI-73 mode screen varies slightly from 
the TI-83 Plus. 



2nd] [FORMAT] 




PolarGC 
CoordOff 
GridOn 

RxesOff 
Label On 

XFfOff 



2. Change the grid setting from GridOff 
to GridOn. 



until GridOff is 
highlighted 

UJ until GridOn is 
highlighted 



IENTERI to select 



PolarGC 
CoordOff 



GridOff M3BMg 
RxesOTT 
Label On 
xprOff 



3. Show the graph screen. Notice both 
the grid and axes are on. 



IGRAPHI 



On Your Own 

(D Change your mode setting ( IMODED to scientific notation (Sci). Do some calculations on the 
Home screen. Try 25*63. Notice how the calculator displays scientific notation. Is this the 
way you write scientific notation? Explain how this setting affects your results. 

(D Turn the grid off on the graph screen. Check this by pressing IGRAPHI . 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 2-3 



i Tip 3: Graphing a Function in the Standard Window 




Tip™ 3: Graphing a Function in the Standard Window 



You can graph a function on the graph screen. First, enter the function in the Y= editor, and then 
you can graph the function in the standard graphing window. Screens on the TI-73 may vary. 



Noti 


Not2 


Plots 


WiH2X+3 




Wz = 






W;= 






Wh = 






We = 






Ws = 






W? = 







Yl=2x+3 in the Y= editor 



WINDOW 
Xnin=-1B 
Xnax=10 
Xscl=l 
Vnin=-1B 
Vnax=10 
Vscl=l 
Xres=l 




Standard Graphing Window 



Graph of Yl=2x+3 



Calculator Keys Used in This § Tip 7 



• IGRAPHI 

• ITRACE] 

1 Tip™ Highlights 

In the d Try-It! example, you will graph a function following these main steps. 



1. 
2. 



Enter the function in the Y= editor (N=\). 

Graph the function on the graph screen ( IGRAPHI ). 

Note: If you reset your calculator defaults (i Tip 1 : Resetting Your Calculator), the graphing window sets up the following 
boundaries for the X and Y values: -10 <X< 10 and"10< Y< 10. 



3. Press |TRACE| . Then press |jj or |T| to move the cursor from one plotted point to another. 
Tracing the graph displays the (X,Y) values at the bottom of the screen. 

For some functions, the graphing window has to be adjusted so that you can see your graph. This 
(D Tip uses the standard window settings (-10 < X < 10 and -10 < Y < 10). The function selected 
for the example on the next page displays the graph in this window. For more information on 
adjusting window settings on the WINDOW menu, see f!) Tip 5: Adjusting the Viewing Window. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 3-1 



i Tip 3: Graphing a Function in the Standard Window 



1 Try-It!™ on Your TI-83 Plus or TI-73 
Enter the Function 

Enter y = 2x + 3 as Yi=2X+3 in the Y= editor. 



Display the Graph 

Display the graph of Yi=2X+3 on the graph screen. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Enter the Y= editor. 

Note: The TI-73 Y= editor varies slightly from the 
TI-83 Plus. The TI-73 lets you enter up to 4 
functions. 


m 










Noti Not2 Plots 

Wi=l 










2. Clear Yi and enter the function, 2X+3. 










ICLEARI 
2|X,T,0,/j|[+l 3 




Noti PlotE Plots 
W1B2X+3 




Note: On the 1 1-/3, use Ul rather than |x,T,e,n|. 

Note: The equal sign next to the function is 
highlighted. This means that the function is selected 
or turned on and will be graphed. If other functions 
are selected, press and [7] as necessary to 
position the cursor over the = sign and press enter 
to turn off the function. 









To Do This 


Press 


Display (TI-83 Plus shown) 


1. Display the graph. 










IGRAPHI 










A 











Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 3-2 



i Tip 3: Graphing a Function in the Standard Window 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Trace the Graph 

Trace the (X,Y) values for Y1=2X+3 on the graph screen. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Enter trace mode. 










ITRACEI 




V1=2K+3 

/ 


V 




/ 


v=3 








2. Trace the (X,Y) values along the 
graph. 

X and Y values display at the bottom 
of the screen. 


and|T) 










V1=2K+3 






/ 

K=i. 7021277 


V=fi.H0H2££3 








3. Quickly find Y when X=-4. 


B4 










V1=2K+3 






J\ 










4. Notice that when X= _ 4 then Y= _ 5. 










IENTERI 




V1=2K+3 






/ 


V="E 




\ Cursor moves 

to (-4, -5). 



On Your Own 

ID Display a grid on the graph screen by selecting GridOn in the window format screen 

([2nd] [FORMAT]). 

1 Define Y2= -X+6. 

(D Graph Yi=2X+3 and Y2= -X+6 at the same time and compare. Now trace along each function 
to find the point of intersection. Record the point of intersection. 

Hint: Use and to move between functions. 

(D Graph Y2 only. 

Hint: You must deselect Yi so that the calculator does not graph it. To deselect Yi , highlight its equal sign (=) in the Y= editor with 
the cursor, and then press I enter] . Notice the equal sign is no longer highlighted. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 3-3 



i Tip 4: Creating a Table 



Tip™ 4: Creating a Table 




You can automatically create a table of values (X,Y) based on functions in the Y= editor. For 
example, if Y=2X+3 is defined in the Y= editor, a corresponding table of (X, Y) values could look 
like this: 



Noti 


Not2 


Plots 


WiH2X+3 




Wz = 






Ws = 






Wh = 






We = 






Ws = 






W? = 







Yl=2x+3 in the Y= editor 



X 


V1 




i 

2 

H 
E 
b 


3 

E 

7 

3 

ii 

13 

IE 




X=0 



Table for Yl=2x+3 



Calculator Keys Used in This i Tip™ 

• [2nd] [TABLE] 

• [2nd] [TBLSET] 

1 Tip™ Highlights 

In the (D Try-It! example, you will display the table values (X,Y) for a function defined in the 
Y= editor following these main steps. 

1. Define a function (Yi=2X+3) in the Y= editor ([W]). 

2. Set up your table in the TABLE SETUP screen ( [2nd] [TBLSET]). 

3. Display the table ([2nd] [TABLE]). 

The following settings in the table setup ( 1 2nd I [TBLSET]) screen determine how the table is 
displayed. 

• TbIStart — First X value. 

• ATbl — Amount by which X values increase and decrease (for example, if ATbl=5, then X 
values increase or decrease by 5). 

• Auto or Ask — Allows you to choose whether or not to display automatically the 
independent (X) or dependent (Y) variable values. 

For more information about table settings, see the calculator guidebook. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 4-1 



i Tip 4: Creating a Table 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Enter the Function 

Enter Yi=2X+3 in the Y= editor flY=T)- See (J) Tip 3: Graphing a Function in the Standard 
Window for step-by-step instructions for defining functions. Your Y= editor should look like this. 



Noti 


PlotE 


Plots 


W1B2X+3 




Wz = 






W;= 






Wh = 






We = 






Ws = 






W? = 







Change the Table Settings 

Define the following settings for your table: TblStart=50 and ATbl=5. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Display the table setup screen. 


[2nd! [TBLSET] 










TRBLE SETUP 

TblStart=0 

^Tbl=l 
Indpnt: KBOZ Rsk 
Depend: sSSSS, Rsk 










2. Change the following settings: 
TblStart=50, ATbl=5. 

Note: lndpnt:Auto and Depend:Auto are the 

defaults. 










ICLEARI 50 


ICLEARI 5 




TRBLE SETUP 

TblStart=50 

^Tbl=5 
Indpnt: ]SS3E Rsk 
Depend: SSSSS, Rsk 











Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 4-2 



i Tip 4: Creating a Table 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Display the Table 

Display the table for Yi=2X+3 on the graph screen. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Display the table. 



2nd] [TABLE] 



X 


Vi 




cn^^M 


105 




ss 


115 




GO 


125 




fi£ 


155 




70 


115 




7£ 


i£5 




BO 


165 




X=50 



2. Scroll through the table values with 
the arrow keys. 

Note: Notice that when you press and move to 
the top of the Yi column, the cursor moves to Yi 
instead of displaying Y-values that are off the 
screen. The function is displayed on the edit line 
and can be changed. 



E,E,B,orE] 

as necessary 



X 


HI 




£0 


105 




££ 


115 




GO 


125 




G£ 


155 




70 


115 




7£ 


i£5 




BO 


1G5 




V1B2X+3 



On Your Own 

ID Try to display more (X,Y) values. Set ATbl=1 (pronounced "delta table") and display the table 
again. Then set ATbl=.1 and display the table. Notice how the table values differ. 

(D Enter Y2=-X+6 in the Y= editor. Display the table of values for both Yi and Y2. Is Yi ever equal 
to Y2? 

Hint: Set TblStart=0 and ATbl =1 and search through the table. 

(D Change the mode ( IMODEQ setting from Normal to Sci. Display the table. Notice how this 
affects the table values. 

d) Go to the table setup screen and figure out what the Depend: Ask setting does. 
Hint: To reveal an invisible Y value in the table, place the cursor on that space and press [enter]. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 4-3 



D Tip 5: Adjusting the Viewing Window 



Tip™ 5: Adjusting the Viewing Window 




You can adjust the viewing window for a specific graph. For example, with the ZStandard 
viewing window default values of -10 < X < 10 and -10 < Y < 10, the graph of Yi=50X appears as 
shown in the screen below on the left. Y increases so rapidly in relation to X that this line is not 
easily seen in this window. You can adjust the window flWINDOWQ values by scaling the 
X axis and Y axis to see the graph in a better perspective. 




Y1=50X viewed 
with the default 
window values. 




Y1=50X viewed with 
adjusted window 
values. 



Calculator Keys Used in This § Tip 7 



IWINDOWI 
[ZOOM] 

Tip™ Highlights 



Window values put specific boundaries on the graph screen. ZOOM flZOOMQ functions 
automatically adjust window values for you; however, you can manually set window values using 
the window ( IWINDOWI ) menu. You can set minimum and maximum X and Y values (Xmin, Xmax, 
Ymin, and Ymax), and you can set the scale (distance between tick marks) of the X axis and Y 
axis (Xscl and Yscl). 

In the d) Try-It! example, you will adjust the viewing window values in two ways. 



Automatically adjust them by selecting a zoom function from the ZOOM ( IZOOMD menu. 



Manually adjust them using the window ( IWINDOWD menu. 



In the example that follows, you see how to change window ( IWINDOWI ) values to see a different 
perspective of the graph of Y1=50X. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 5-1 



D Tip 5: Adjusting the Viewing Window 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Enter the Function 

Enter Yi=50X in the Y= editor ([Y=]). See fj) Tip 3: Graphing a Function in the Standard Window 
for step-by-step instructions for defining functions. Your Y= editor should look like this. 



Noti 


PlotE 


Plots 


W1B50X 




Wz = 






W;= 






Wh = 






We = 






Ws = 






W? = 







Display the Function on the Graph Screen 

Note: The window values shown here are the default window values, also equivalent to ZStandard ( |zoom| ) (-10 < x < 10; -10 < Y < 10). 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Graph Yi. 










IGRAPHI 




















2. Display the window settings menu. 

Note: This window shows (X,Y) values so that 
-10<X< 10 and -10 < Y< 10. This is equivalent to 
the default ZStandard setting. 










IWIND0WI 




WINDOW 
Xnin=-10 
Xnax=10 
Xscl=l 
Vnin=-10 
Ynax=10 
Vscl=l 
Xres=l 











Define a Different Viewing Window for Your Graph 

View the table of (X, Y) values created by Yi =50X to help you redefine window values. Start the 
table at _ 3 and increment the values by 1. See (D Tip 4: Creating a Table for step-by-step 
instructions for creating a table. 

Tip: You can choose any X values for the table. For this exercise, you view a table of values when -3 < X < 3. When you set the table to 
start at -3 with increments of 1 , you can see the relationship between X and Y near the origin of the graph. 

Your table should look like this: 



X 


Vi 




S^^H 


-i£0 




-2 


-100 




-i 


-£0 












i 


£0 




2 


100 




3 


i£0 




X="3 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 5-2 



D Tip 5: Adjusting the Viewing Window 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Define a Different Viewing Window for Your Graph (continued) 



Notice in the table that when -3 < X < 3, the Y values range from -150 < Y <150. Since Y increases 
by 50 each time X increases by 1, you can set the Yscl to 50 and leave Xscl set at 1. Now, create a 
window to see the graph for this domain and range by changing the window values. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Display the window settings screen. 

Note: Window settings screen is slightly different on 
the TI-73. 



IWINDOWI 



WINDOW 
Xnin=-10 
Xnax=10 
Xscl=l 
Ynin=-10 
Ynax=10 
Yscl=l 
Xres=l 



2. Define the values so that Xmin = -3, 
Xmax = 3, Xscl = 1,Ymin = -150, 
Ymax = 150, and Yscl = 50. 

Note: This changes the settings so that: 
-3 < X < 3 and -150 < Y < 150. Since Xscl=1 and 
Yscl=50, there is one unit between each tick mark 
on the X axis and 50 units between each tick mark 
on the Y axis. 

TI-73: AX scales automatically, based on Xmin and 
Xmax. See the calculator guidebook for details. 



© 3 (to Xmax) 
3 (to Ymin) 

© 150Q (to Ymax) 
150 (to Yscl) 
50 



WINDOW 
Xnin=-3 
Xnax=3 
Xscl=l 
Ynin=-150 
Ynax=150 
Yscl =50 
Xres=l 



3. Graph Yi =50X in this different 
window. 

Note: Remember that each tick mark on the X axis 
represents 1 unit, while each one on the Y axis 
represents 50. It's always important to know the 
scale of your graphs so that you understand the 
graph you are viewing. 



IGRAPHI 




4. Trace the graph. 



TRACE 



Note: Each tick mark on the X axis is 1 and on the 
Y axis is 50. 



or as necessary 



V1=£0K 




K=.B297B723 


V=1i.HB93fi2 



5. Display the Y value when X=2. 

Tip: You can go directly to any coordinate pair on 
the graph by entering the value you want. 



ENTER 



V1=£0K 




X=2 





V1=£0K 


y 


K=2 


V=i00 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 5-3 



D Tip 5: Adjusting the Viewing Window 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Using ZDecimal — the Friendly Window 

• Display and trace the graph Y2=2x, using ZDecimal window values. ZDecimal lets you trace 
the X values by tenths (.1, .2, .3, . . .). 

• Multiply Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl by 100 in the window menu, and trace the 
function. This lets you trace the X values by tens. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Turn off the graph and table of 
Yi=50X and enter Y2=2x in the 
Y= editor. 

Note: On the TI-73, use \x\ rather than |x,T,e,n| . 



|T| |ENTER| 

BHfCLEAR] 

2|X,T,Q,/7| 



M*ti Not2 Plots 
Wl=50X 

WeB2X 



2. Graph Y2=2x using ZDecimal window 
values. 



[ZOOM] 

until ZDecimal is 
highlighted 

1 ENTER I 




3. Trace the graph. 

Note: Notice that the window is set up so that the X 
values are tracing by tenths. 



ITRACEI 

UJ or UJ as necessary 



V2=2K 


V 


„ A 


V=i.H 



4. Multiply Xmin, Xmax, Xscl, Ymin, 
Ymax, and Yscl by 100. 

Tip: Press [2nd] UJ to move the cursor to the end of 
a window setting line. 

Note: TI-83 Plus: See the calculator guidebook for 
details about Xres. It is not discussed in this 1 Tip. 
TI-73: See the calculator guidebook for details 
about AX. It is not discussed in this § Tip. 



IWINDOWI 

Repeat for each value: 

f2nd1 |T1 

0100 

I ENTER I 



WINDOW 
Xnin=-470 
Xnax=470 
Xscl=100 
Ynin=-310 
Ynax=310 
Vscl=100 
Xres=l 



5. Trace the graph. 

Note: Notice that the window is set up so that the X 
values are tracing by tens. 



ITRACEI 

UJ or UJ as necessary 



V2=2K 


V 


K=90 / 


V=iB0 



On Your Own 

(D Graph Yi=.1X. How can you set an appropriate viewing window for this graph? 

Hint: Make a table of values for Yi=.1X and use the table information to change the window values. Try finding the best values to choose 
when -5<X<5. If X=5, Y=.1(5)=.5. Therefore, the Y values need to be very small. Try changing Ymin, Ymax, and Yscl. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 5-4 



I Tip 6: Using Lists 



Tip™ 6: Using Lists 




You can enter lists of different kinds of data into the list editor. For example, let's look at two 
students' test scores. 

• Jamal's test scores are 80, 85, 90, 75, and 85. 

• Jian's test scores are 85, 70, 75, 95, and 100. 

You can create two separate lists in the list editor containing these scores. Then, on the Home 
screen, you can find the sum of the elements of both lists, and then divide by the number of 
elements (5) to calculate each student's test average or mean. 

You can find the 
mean or median on 



Li lists Jamal's 


L1 


L2 


L3 2 


B0 
\BE 

7E 
BE 


BE 
70 
7E 
BE 
100 




scores. 




L2(fil = 



meant L 2 > 



85 



the Home screen. 



Calculator Keys Used in This i Tip™ 

• [2nd] [CATALOG] (to access the ClearAIILists and SetUpEditor commands) 



• TI-83 Plus: [2nd] [LIST], [sTATI 

• TI-73: EST], [2nd] [STAT] 

1 Tip™ Highlights 

Both the TI-83 Plus and the TI-73 have two menus — OPS and MATH — that contain various list 
commands that help you find mean, median, and much more. For more information on all menu 
items, see the calculator guidebook. 



TI-83 Plus: 

[2ndl [LIST] E UJ 



NAMES OPS WOB. 

l:nint 

2:naxC 

sflroeant 

4: nediant 

5: sunt 

6: prod C 

7-i-stdDeuC 



TI-73: 

[2nd] [STAT] [7J 



Ls OPS WOB. CflLC 

l!nin< 

2:naxC 

§flnean( 

4! nediant 

5: node <! 

6:stdDeu( 

7: sunt 



In the (D Try-It! example, you will use the ClearAIILists and SetUpEditor commands, which are 
located in the CATALOG ( [2nd] [CATALOG]) on both the TI-83 Plus and the TI-73. These commands 
clear and set up the list editor as described below. 

• ClearAIILists erases all elements of all existing lists on your calculator. The list names are still 
in memory, but the lists are empty. You cannot get the list elements back. 

• SetUpEditor removes all list names from the list editor except the default list names, Li 
through L6. It also creates one blank list after L6. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 



© 2001 Texas Instruments 



I Tip 6-1 



I Tip 6: Using Lists 



1 Try-It!™ on Your TI-83 Plus or TI-73 
Set Up the List Editor 

Use the commands ClearAIILists and SetUpEditor to reset the list editor. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Display the list editor. 

Note: Your list editor may vary. The following 
commands will clear and set up lists L1 through L6 
in your list editor. 


TI-83 Plus: 










RED 


BLUE 


■n h 




12 
6 


3 

9 




|STAT| 1:Edit 

TI-73: 

|LIST| 


Hane= 








2. Return to the Home screen and clear 
it. Then clear all lists in the list editor 
by selecting ClearAIILists. 

Note: This command clears all elements from the 
lists. The list names are still in memory, but the lists 
are empty. 

Hint: In the CATALOG, you can go to the first item 
starting with a particular letter: 

TI-83 Plus: Press C (|prgm|). Notice that you are 
already in ALPHA mode since the displays in the 
upper right corner. 

TI-73: Press [2nd] [text], highlight C, and then press 

lENTERl. 










|2nd| IQUITI |CLEAR| 
[2nd] [CATALOG] 

until ClrAIILIsts is 
selected 




CRTRLOG H 

X2cdf< 

X2pdf< 

X * -TestC 

Circlet 

Clear Entries 
►ClrRllLists 

ClrDraw 










lENTERl 




ClrRllLists 

Done 




lENTERl 


3. Setup the list editor with SetUpEditor. 

Hint: You also can select SetUpEditor on the 
TI-83 Plus by pressing [sTaT] 5. 


[2nd] [CATALOG] 

until you highlight 

SetUpEditor 










CRTRLOG H 

SelectC 

SendC 

se^K 

Se^i 

Sequential 
► SetUpEditor 

Shade < 




lENTERl 








lENTERl 




ClrRllLists 

Done 
SetUpEditor 

Done 

I 










4. Display the list editor. 

Note: Lists Li through L6 appear and are clear, and 
there is a blank list following L6. 


TI-83 Plus: 










L1 


L2 


L3 1 










|STAT| 1:Edit 

TI-73: 

|LIST| 


L1(1J = 










L£ j 


Lb 


wmm ? 










Hane= 









Topics in Algebra 1 



© 2001 Texas Instruments 



| Tip 6-2 



I Tip 6: Using Lists 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

Enter the Lists 

In the list editor, enter Jamal's scores as Li ={80,85,90,75,85} and Jian's scores as 
L2={85,70,75,95,100}. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Enter data into Li . 


80 

85 
90 
75 
85 










L1 


L2 


L3 1 




B0 
BE 
90 






L1(fiJ= 








2. Enter data into L2. 


(to place the cursor 
under L2) 

85 
70 
75 
95 
100 










L1 


L2 


L3 2 




B0 
BE 
90 
?E 
BE 


BE 
70 
7E 
9E 
100^^ 




L2(fil = 









Topics in Algebra 1 



© 2001 Texas Instruments 



1 Tip 6-3 



I Tip 6: Using Lists 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Display the Sum and Average of All Elements in a List 

On the Home screen, find the sum of Jian's test scores (L2). 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Return to the Home screen and clear 
the current line, if needed. 

Tip: Once you exit the application, you can press 
[Ml [quit] to return to the Home screen from any 
menu or command. 






|2nd| IQUITI ICLEARI 


2. Select sum( from the MATH menu. 


TI-83 Plus: 

m [list] uj uj 

5:sum( 

TI-73: 

[2nd] [STAT] [7J |JJ 

7:sum( 










HRMES OPS UHli 
1 : Mint 
2:MaxC 
3: Meant 
4: Mediant 

SflSUMt 

6: prod C 
7-i-stdDeut: 












SUMt 




3. Select the list (L2) you want, and 
display the sum. 


TI-83 Plus: 

[2nd] [LIST] 

2:L2Q] 

lENTERl 

TI-73: 
[2nd] [STAT] 
2:L2Q] 
lENTERl 










sum^LzJ 

425 










4. Divide L2 by 5 (the number of test 
scores) to find the average (or mean) 
of the list of the scores. 

Note: Ans is the previous answer, 425. 


E5 

^™J Ans = 425 . 










sum^Lz} 

425 
fins/5 

35 











Topics in Algebra 1 



© 2001 Texas Instruments 



1 Tip 6-4 



I Tip 6: Using Lists 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Find the Mean and Median of a Set of Data 

On the Home screen, find the mean and median of Jamal's test scores 



O-i). 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Return to the Home screen and clear 
the current line, if needed. 






|2nd] IQUITI |CLEAR| 


2. Select mean( from the MATH menu. 


TI-83 Plus: 

\M [list] B B 

3:mean( 

TI-73: 

[2nd] [STAT] |TJ |JJ 

3:mean( 










HRMES OPS UHli 

l!nin< 

2:naxC 

§flnean( 

4! nediant 

5: sunt 

6: prod C 

7-i-stdDeuC 










3. Select the list (Li) that you want, and 
then calculate the mean. 


TI-83 Plus: 
[2nd] [LIST] 1 :L1 
lENTERl 

TI-73: 

[2nd] [STAT] 1 ±1 

lENTERl 










neantLi !> 

S3 










4. Select median( from the MATH menu. 


TI-83 Plus: 
[2nd! [LIST] B B 
4:median( 

TI-73: 

[2nd! [STAT] B B 

4:median( 










HRMES OPS WOll 

l!nin< 

2:naxC 

3: neant 

Sflnediant 

5! sunt 

6: prod C 

7istdDeyC 










5. Select the list (Li) that you want, and 
then display the median. 


TI-83 Plus: 
[2nd] [LIST] 1 ±1 
lENTERl 

TI-73: 

[2nd] [STAT] 1 ±1 

lENTERl 










neantLi > 

S3 
median tLi > 

S5 











Topics in Algebra 1 



© 2001 Texas Instruments 



1 Tip 6-5 



I Tip 6: Using Lists 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

On Your Own 

ID Calculate the 1-variable statistics analysis for Li using the 1 -Var Stats command on the Home 
screen. Use the arrow keys (0 and 0) to view all of the information about Li. 

Select the 1 -Var Stats command from this menu: 



• TI-83 Plus: ISTATI CALC menu 

• TI-73: [2nd] [STAT] CALC menu 

Hint: Select the 1-Var Stats command first, and then select L1. For more information about 1-Var Stats seethe calculator 
guidebook. 

(D If you are already familiar with statistical plots, find the quartile statistics in the list of data 
that was generated above, and draw a box plot of the data. For help, see (§ Tip 7: Creating a 
Statistical Plot. 



Topics in Algebra 1 © 2001 Texas Instruments i Tip 6-6 



i Tip 7: Creating a Statistical Plot 



Tip™ 7: Creating a Statistical Plot 




Statistical plots are graphs of data values that have been stored in lists. You can create several 
types of statistical plots, such as scatter plots, histograms, box plots, and pie charts (TI-73 only). 




Scatter Plot 



Histogram 



P2:L2 



MinX=fi3 



Box Plot 



i 


10 






2 


33 






3 


£0 


{ b 




H 


22 




J 2 t 


£ 


IE 




fi:37 


\ V J / 


L1:BH 


L2:iE 



Pie Chart (TI-73 only) 



Calculator Keys Used in This 1 Tip™ 

• TI-73: [2nd] [PLOT] 

• TI-83 Plus: [2nd] [STAT PLOT] 

• [ZOOM] ZoomStat 

1 Tip™ Highlights 

In the d) Try-It! example, you will graph a statistical plot following these main steps. 

1. Enter all necessary lists in the list editor. 

2. Define your statistical plot in the stat plot editor. 

3. Display the statistical plot by pressing |Z00M| (ZoomStat). 



Pressing |TRACE| allows you to move the cursor from one plotted point to another using [jj and [TJ. 
It also displays the values (X,Y) at the bottom of the screen. For more information about 
statistical plot options, see the calculator guidebook. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 7-1 



i Tip 7: Creating a Statistical Plot 



1 Try-It!™ on Your TI-83 Plus or TI-73 

You have collected the measurements (in inches) of how far a boy from age 5 to age 14 could 
throw a ball above his head. The following data was recorded. Create a scatter plot (Li_) based 
on these lists, where Li = Age in years and L2 = Distance in inches. 



Age in years (L1) 


Distance in inches (L2) 


5 


66.9 


8 


75.8 


9 


77.7 


10 


79.9 


12 


85.8 


14 


91.7 


Enter the Lists in the List Editor 



See (D Tip 6: Using Lists for step-by-step instructions for entering lists of data (remember to use 
ClearAIILists and SetUpEditor). Your list editor should look like this: 



L1 


L2 


L3 2 


£ 


bb.9 




B 


7E.B 




9 


??.? 




10 


79.9 




12 


B5.B 




11 


UAm 




1.2(71 = 



Define the Statistical Plot 

Define Plotl as a scatter (Lil) plot where Xlist=Li and Ylist=L2. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Display the STAT PLOTS screen. 


TI-83 Plus: 

[2nd] [STAT PLOT] 

TI-73: 

[2nd] [PLOT] 










am«HH; 




[flp~"rJ5ff 

I--' L1 L2 d 

2:Plot2...0ff 

I--' L1 L2 d 

3:Plot3...0ff 

I--' L1 L2 d 

4-i-PlotsOff 








2. Display the Plotl settings screen. 


1:Plot1 










JfSS\ Not2 Plots 

DntffiH 
TypeT™ k± Jhb 

*■■ CD-" |^~ 

XlisULi 
Vlist:L2 
Mark: B ♦ ■ 










3. Select On to turn on Plotl . 

Note: Scatter (Lei), is already selected because 
you reset the calculator for this § Tip. Xlist and 
Ylist do not have to be changed because, by 
default, they already match our selected lists. 










IENTERI 




3HH Pi*t2 Plots 

Sfiroff 

Type: BH l^ Jh. 

*■■ dH |^~ 

Xlist:Li 
Vlist:L2 
Mark: B + ■ 











Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 7-2 



i Tip 7: Creating a Statistical Plot 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Display the Statistical Plot on the Graph Screen 

Display the statistical plot on the graph screen using the ZoomStat command and trace it. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Select ZoomStat from the ZOOM 
menu. 


TI-83 Plus: 

|Z00M| 

9:ZoomStat 

TI-73: 
|Z00M| 
7:ZoomStat 










BMBj MEMORV 

4tZDecinal 

5:ZS^iuare 

i:ZStandard 

7:ZTri9 

3:ZInte9er 

SflZoonStat 

JiZoonFit 












D 

D 

D 
D 
D 

D 










2. Trace along the statistical plot. 

Note: P1 :Li,L2 in the upper left corner shows that 
the lists Li and L2 contain the data for the graph. 
The data points are displayed at the bottom of the 
screen. 






ITRACEI 

UJ or [JJ as necessary 




— L1 and L2 contain tne 
data for this graph. 


PiiLIAZ 

D 
D 

D 




(X,Y) coordinates of 
— the data point at the 
cursor location. 



Topics in Algebra 1 



©2001 Texas Instruments 



I Tip 7-3 



i Tip 7: Creating a Statistical Plot 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 

On Your Own 

1. Enter the following math test scores in Li and L2. 



2. 
3. 



Scores (L1) 


Frequency (L2) 


99 


4 


96 


4 


92 


3 


88 


2 


84 


3 


78 


2 


74 


2 


70 


1 


66 


1 


64 


1 



Set up the histogram ( Jkb ) where Xlist=Li and Freq=L2 in the STAT PLOTS menu. 



Graph the histogram using Zoom Stat, and then trace ( I TRACED the histogram. Letter grades 
correspond to these test scores: A = 100-90; B = 89-80; C = 79-70; D = 69-60; F = 59-0. Did 
the graph display the way you expected? Why is it necessary to change the window values 
manually? 

4. Change the window values manually to group the data in intervals of 10. Remember that you 
want the data grouped in intervals of 10 so you can see how many test scores fall into the 
grade categories given above. You can tell the calculator to do this by setting Xscl=10 on the 
graphing window ( IWINDOWD . Xmin should be a little less than the lowest score and Xmax 
should be a little higher than the highest score to display a nice graph. Try setting the window 
as Xmin=50, Xmax=100, Ymin= -4, Ymax=15, and Yscl=10. 

5. Graph and trace the histogram again to see why these settings show the grades grouped by 
scores that match the letter grades A, B, C, D, and F. 

Hint: Remember that if you have functions defined and turned on in the Y= editor, the calculator graphs these at the same time as the stat 
plot. To turn off a function, highlight the = sign next to it, and then press [enter]. 

Or you can select FnOff. To do this: 

• On the TI-83 Plus: Press [vars] H 4:On/Off 2:FnOff 

• On the TI-73: Press [2nd] [vars] 2:Y-Vars 6: FnOff 



Topics in Algebra 1 



©2001 Texas Instruments 



| Tip 7-4 



Tip 8: Finding the Best Line of Fit for a Set of Data 



Tip™ 8: Finding the Best Line of Fit for a Set of Data 




Both the TI-83 Plus and the TI-73 have regression commands that automatically find the closest 
equation to your statistical plot data. The LinReg(ax+b) command finds the closest linear 
equation y=ax+b and displays the values for a (slope) and b (y-intercept) on the Home screen. 

You can save this equation in the Y= editor so that you can graph the regression equation and the 
statistical plot data at the same time, and then compare the two. 



Pi:L1A2 




K=iO 7=79.9 



Statistical plot data points 

Linear Regression line based 
on statistical plot data 



Calculator Keys Used in This i Tip™ 

• TI-83 Plus: [STATI (CALC menu) LinReg(ax+b) 

• TI-73: Und] [STAT] fj] (CALC menu) LinReg(ax+b) 

1 Tip™ Highlights 

This (D Tip shows you how to use LinReg(ax+b) on the Home screen to find the linear regression 
of two list names, XList (Li) and YList 0-2). You will use the same list values that you used to 
define the statistical plot. 

Note: For more information about statistical plots, see § Tip 7: Creating a Statistical Plot. 

In the d) Try-It! example, you will find a linear regression following these main steps. 



1. Select LinReg(ax+b) from the I STAT I CALC menu. 

2. Enter the two list names that define the statistical plot. 

3. Save the equation in the Y= editor. 

4. Graph the statistical plot and the linear regression. 

Note: The examples in the next section assume that the calculator has been reset to the default settings as described in 
i Tip 1 : Resetting Your Calculator. 



Topics in Algebra 1 © 2001 Texas Instruments i Tip 8-1 



Tip 8: Finding the Best Line of Fit for a Set of Data 



1 Try-It!™ on Your TI-83 Plus or TI-73 

You have collected the measurements (in inches) of how far a boy could throw a ball above his 
head from age 5 to age 14. The following data was recorded. Create a scatter (kil) plot based on 
these lists, where Xlist=Li and YList= L2. 



Age in years (Li) 


Distance in inches (1-2) 


5 


66.9 


8 


75.8 


9 


77.7 


10 


79.9 


12 


85.8 


14 


91.7 



Enter the Lists for the Statistical Plot 

See (D Tip 6: Using Lists for step-by-step instructions for entering lists of data. Your list editor 
should look like this: 



L1 


L2 


L3 2 


£ 


bb.S 




B 


7E.B 




9 


??.? 




10 


79.9 




12 


B5.B 




1H 


tkim 




1.2(71 = 



Create a Scatter Statistical Plot for L1 and L2 

See fl| Tip 7: Creating a Statistical Plot for step-by-step instructions for creating a scatter 
statistical plot. Your statistical plot editor and scatter plot (using ZoomStat) should look like this: 



Not2 Plots 

Off 
ype: IB L± Jb, 

>0<" >DH |^~ 

Xlist:Li 
Vlist:L2 
Mark: B + • 




Stat Plot Editor Graph of Plot 

Note: The stat plot editor in the TI-73 looks slightly different. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 8-2 



Tip 8: Finding the Best Line of Fit for a Set of Data 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Find the Linear Regression for the Scatter Plot 

Find the regression (the line which best fits the data) for Li and L2 using LinReg(ax+b). 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Return to the Home screen, and clear 
it. 






|2nd| IQUITI |CLEAR| 


2. Select LinReg(ax+b) from the STAT 
CALC menu. 


TI-83 Plus: 
I ST AT | fTJ 
4:LinReg(ax+b) 

TI-73: 

[2nd] [STAT] [TJ 

5:LinReg(ax+b) 










EDIT WSlBj TESTS 

l:l-VarStats 

2:2-Uar Stats 

3:Med-Med 

SBLinRegCax+b> 

STQuadReg 

6:CubicReg 

7iQuartReg 












LinRegCax+b) 




3. Select the lists Li and L2. 


TI-83 Plus: 
[2nd] [LIST] 1 ±1 Q 
[2nd] [LIST] 2 ±2 [7] 

TI-73: 

[2nd] [STAT] 1 ±1 □ 

[2nd] [STAT] 2 ±2 [7J 










LinRegCax+b) Li , 
Lz 




4. Display Y-VARS menu. Then select 
the Y variable (Y1) from the 
FUNCTION menu. 

5. Calculate the regression equation. 


TI-83 Plus: 
|VARS|U] 
1 :Function 
1:Y1 

lENTERl 

TI-73: 

[2nd] [VARS] 2:Y-Vars 

1:Y1 

lENTERl 










LinRegCax+b> Li , 




LinReg 
y=ax+b 

a=2. 713513514 
b=53. 4027027 


6. Display the Y= editor. 

Note: Both Y1 and Plotl are highlighted. This 
means that both graph and the plot are turned on. 


m 










iJ^n pi^tE plots 
WiB2. 7135135135 
137X+53. 40270270 
27 
Wj = 
Wj = 
Wh = 











Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 8-3 



Tip 8: Finding the Best Line of Fit for a Set of Data 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Graph the Statistical Plot and the Linear Regression 

Graph and trace the statistical plot and linear regression at the same time and compare them. 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. Select the ZoomStat function to 
display the statistical plot and the 
regression on the graph screen at the 
same time. 



TI-83 Plus: 

[ZOOM] 

9:ZoomStat 

TI-73 : 
[ZOOM] 
7:ZoomStat 



MEMORY 
eciroal 
5:ZS°njare 
6:ZStandard 
7:ZTri9 
SiZ Integer 
ZoonStat 
ZoonFit 




2. Trace the function or the statistical 
plot. 

Notes: The function or plot being traced is 
displayed in the upper left corner of the screen. The 
X and Y coordinates display at the bottom of the 
screen. 



ITRACEI 

H or |T| to trace a 

function 

and to move 

between functions 



Pi:L1A2 




K=iO 



1=79.9 



Tracing along the stat plot 



V1=2.ri3£i3£i3£i37K+£3.H- 




K=9.£ 



Y=79.iBiOBi 



Tracing along the line 



On Your Own 

ID Use the function to predict approximately how far you think the boy can throw the ball 
above his head at 18 years old. Do you think the line will give a good idea of how high this 
person will be able to throw the ball when he is 35? Explain your thoughts. 

Hint: Use the table to determine the value of Yi when X=18. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 8-4 



d Tip 9: Sending and Receiving Data between Calculators 



Tip™ 9: Sending and Receiving Data between Calculators 

You can send and receive data between calculators using the SEND and RECEIVE menus. 

To connect two calculators using the unit-to-unit cable, which comes packaged with your 
calculator, use the I/O (input/output) port located at the center of the bottom edge of the 
calculator. 

• Insert either end of the unit-to-unit cable into the I/O calculator port. 

• Insert the other end of the cable into the I/O port of the other calculator. 

Tip: The cable must be firmly inserted into the I/O port. If you receive a "link error," make sure the cable is completely inserted. 

Sending unit Receiving unit 




Q S &E! i.^.i :~0 

cbq 
tDi±5 

rate) 

1V1 :V, 



ooco 

GDdJCD 





BDB3E3B3E3 
BBBaiE) 
feCDCDCIDCiD 

HciiciJHiczi 
5bcd[z3sc3 

BEHZji": 




I/O ports for cable 

Calculator Keys Used in This D Tip 7 

• TI-83 Plus: [2nd] [LINK] 



• TI-73: [APPSl 1 :Link 

1 Tip™ Highlights 

You can send or receive many types of data such as lists, programs, pictures, and applications 
that can be shared. 

To communicate between two calculators, you must set up one calculator to send the data and 
the other calculator to receive the data. 

Note: You can only link two TI-73 calculators or two TI-83 Plus calculators. You cannot link a TI-73 and a TI-83 Plus. 



Topics in Algebra 1 



© 2001 Texas Instruments 



| Tip 9-1 



d Tip 9: Sending and Receiving Data between Calculators 



§ Tip Highlights (continued) 

In the (D Try-It! example, you will link two calculators and send lists of data from one calculator 
to the other following these main steps. 

Receiving Data 

After you link the calculators using the unit-to-unit cable, set up one calculator to receive data by 
following these steps: 



1. Display the link menu. 
• TI-83 Plus: [2nd] [LINK] 



• TI-73: [APPSl 1 :Link 
2. Press [jj to display the RECEIVE menu. 



3. Select 1 :Receive. The message Waiting... and the busy indicator are displayed. The calculator 
is ready to receive transmitted items. 

Sending Data 

After you link the calculators using the unit-to-unit cable and have one calculator waiting to 
receive data, set up the other calculator to send data by following these steps: 

1. Display the link menu. 

• TI-83 Plus: [2nd] [LINK] 

• TI-73: [APPSl 1 :Link 

2. Select the type of data (for example, lists) that you want to send. The corresponding SELECT 
screen is displayed. Each SELECT screen is displayed initially with no items selected. 

Note: The AII+ menu item selects all items on your calculator that can be transmitted. The All- menu item deselects all items that 
you have selected to transmit. 



Select the 
type of data. 



aaaii: r 
nTTTi+ 



RECEIVE 



2: fill-... 

3:Pr9n... 

SHList... 

5? Lists to TIS2.. 

6:GDB... 

7-i-Pic... 



sMMXHi TRANSMIT 

rti LIST 

Le list 

Ls LIST 

Lh LIST 

Le LIST 

Ls LIST 



All lists on the 
calculator are 
displayed. 



3. Press and to move the selection cursor (►) to an item you want to select or deselect. 



4. Press |ENTER| to select or deselect an item. Selected names are marked with a box (■). You can 
select more than one if you want. 



Topics in Algebra 1 



© 2001 Texas Instruments 



1 Tip 9-2 



d Tip 9: Sending and Receiving Data between Calculators 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Transfer Li and L2 from one calculator to another one. Use Li and l_2 as defined in 
fj) Tip 6: Using Lists. 

• L1 ={80,85,90,75,85} 

• L2={85,70,75,95,100} 



To Do This 



Press 



Display (TI-83 Plus shown) 



1. On the sending calculator, enter the 
lists above in the list editor. 



TI-83 Plus: 
[STATI 1:Edit 

TI-73: 



L1 


L2 


L3 2 


BO 


BE 




BE 


70 




90 


7E 




7E 


9E 




BE 


100^^ 




L2£fi) = 



2. Link the two calculators using the 
unit-to-unit cable. 



Sending unit 



Receiving unit 



b6bW 

BBBBS 
0BBQi3 
ODBJCDCBCB 
H CzD BO BO BO 
BO BO BO BO BO 
BO BO BO BO BO 
BO BO BO BO g3 



' :K :-.:..'- 



ED BO ED 
BOBOEO 
BO BO BO 
BOBOEO 
BO ED ED 

ededeo 

(EDEDEO 
EOEDEO 
EOEOED 



E B 

b:" b. 

BDEO 
B V 
ED'e 
B B 

=: - 



Connect the calculators with 
the cable using the I/O ports. 



3. On the receiving calculator, select 
Receive. 

Confirm that Waiting... is displayed 
on the screen. Your calculator is now 
ready to receive the lists. 



TI-83 Plus: 
[2nd] [LINK] 
UJ 1 : Receive 

TI-73 : 

[APPSl 1:Link 
E 1 : Receive 



SEND laiOMIMa 
iHReceiue 



4. On the sending calculator, display the 
SEND menu, and then select List. 



TI-83 Plus: 
[2nd] [LINK] 
4: List 

TI-73 : 

[APPSl 1:Link 
4: List 



aaaii: r 
nTTTi+ 



RECEIVE 



2: fill-... 

3:Pr9n... 

JBList... 

5? Lists to TIS2.. 

6:GDB... 

7-i-Pic... 



5. Select Li and L2. 

Note: The selected lists are marked with a box (■). 



ENTER 



lENTERl 



a=i«=Mi 


TRANSMIT 
LIST 


■ Li 


■ Le 


LIST 


► Ls 


LIST 


Lh 


LIST 


Le 


LIST 


Lb 


LIST 



Topics in Algebra 1 



© 2001 Texas Instruments 



| Tip 9-3 



d Tip 9: Sending and Receiving Data between Calculators 



Try-It!™ on Your TI-83 Plus or TI-73 (continued) 



6. Send the lists to the receiving 

calculator using the TRANSMIT menu. 


E 

1 :Transmit 










SELECT U&UHfilll 
iHTransMit 










7. If the lists have been previously 

defined, the receiving calculator asks 
you if you want to: 

1 : Rename 
2: Overwrite 
3: Omit 
4: Quit 

Select Overwrite for each list. 


2:Overwrite 










■11 lp t GEM3 ! ET3T3 




1 : Rename 
fflOuerwi-ite 
3: On it 
4:Quit 

Li LIST 








The name and type of each data 
item are displayed line by line on 
the sending unit as the item is 
transmitted, and then on the 
receiving unit as each item is 
accepted. 

After both lists are transmitted, 
the message, Done, is displayed 
on both calculators. 












Li LIST 
► Lz LIST 
Done 

Sending calculator 




Receiving... 
Li LIST 
► Lz LIST 
Done 

Receiving calculator 



On Your Own 

(D Enter a function in the Y= editor and send it to another calculator. 



Topics in Algebra 1 



© 2001 Texas Instruments 



1 Tip 9-4 



§ Tip 10: Managing Your Calculator's Memory 



• 



Tip™ 10: Managing Your Calculator's Memory 




You can check available memory, manage memory, and get information about your calculator by 
selecting items from the 1 2nd I [MEM] MEMORY menu. For example, you can find your calculator ID 
number, which is necessary for registering and installing some applications. A delete menu item 
lets you delete any type of data (variables, lists, programs, applications, etc.) so that you can set 
up your calculator with the information you need for your current classes. You can change the 
data for future classes. 



SBflbout 




SBflbout 


2: Men Mgmt/Del... 




2i Check RAM... 


3: Clear Entries 




3: Check HPPs... 


4:Clrfllll_ists 




4: Delete... 


5:firchiue 




5: Clear Hone 


6:Unfirchiue 




6:Clrfllll_ists 


7-1-Reset... 




7: Reset... 


TI-83 Plus 




TI-73 



Calculator Keys Used in This § Tip 7 

[2nd] [MEM] 



1 Tip™ Highlights 

The About screen displays: 

• Your calculator operating system version number 

• Your calculator ID number, which is used to register and install or reinstall an application 



The operating system 
version number 



TI-BSPlus 

i.iz 

PROD.ID:0H-0-0i-0C 
ID:0H0BH-9C399-7EB1 
Cert. Revision #i 



Htlp: www.ti.corvii'calc 



GRAPH EXPLORER SOFTWARE 

i.10 
PROD.ID:02-0-0i-2B 

ID:0£0CB-fiFEHD-A0F0 

C*Kt. Revision ttl 



Htlp: www.ti.conii'calc 



The calculator ID number 



TI-83 Plus 



TI-73 



As new operating system versions become available, you can download them from the Texas 
Instruments website. To obtain some applications from Texas Instruments, you must provide 
your calculator ID number, which is unique to your calculator. 

The Mem Mgmt/Del menu item lets you delete variables, lists, programs, applications, etc., so that 
you can set up your calculator with the information you need for your current classes. 

The Reset menu item lets you reset your calculator default settings. Resetting all RAM on your 
calculator: 

• Restores memory to the factory settings. 

• Deletes all programs. 

Note: Resetting RAM does NOT erase applications. 

To find out more about resetting defaults, see (§ Tip 1: Resetting Your Calculator. 



Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 10-1 



§ Tip 10: Managing Your Calculator's Memory 



1 Try-It!™ on Your TI-83 Plus or TI-73 

Displaying the About Screen 

Display your calculator's About screen and find the operating system version number and the ID 
number. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Select About from the MEMORY 
menu. 


[2nd] [MEM] 
1 :About 










SBflbout 

2: Men M9nt^Del... 

3: Clear Entries 

4:Clrfilll_ists 

5 : firch i ue 

6:Unfirchiue 

7-i-Reset... 










2. Notice the operating system version 
number under the name of the 
calculator (1 .12) and the ID number 
composed of 14 numbers and letters. 












TI-B3P1US 
1.12 
PR[]D.ID:0H-0-0i-0C 
ID:0H0BH-9C399-7EB1 
Cert. Revision #1 

Help: www.ti.corvii'calc 











Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 10-2 



§ Tip 10: Managing Your Calculator's Memory 



i Try-It!™ on Your TI-83 Plus or TI-73 (continued) 
Deleting Items 

Delete L4 from your calculator's memory. 



To Do This 


Press 


Display (TI-83 Plus shown) 


1. Display the MEMORY menu and select 
Mem Mgmt/Del. 


TI-83 Plus: 

[2nd] [MEM] 










iMMa 


ft 
At 

Mgrnt/Del... 




1 : Rboi 
ifflMen 


Note: The TI-73 screen looks somewhat different. 


2:Mem Mgmt/Del 

TI-73: 

[2nd] [MEM] 




3: Clear Entries 
4:ClrRllLists 
5s Archive 
6:UnRrcr,ive 
7-1-Reset... 










4: Delete 




2. Select the category, List. 


TI-83 Plus: 










RRM FREE 23489 










RRC FREE 131072 




All existing lists on your calculator 


4:List 




1 = Rl 1... 

2: Real... 




display on this screen and the number 
of bytes of RAM that they use (Li=66 


TI-73: 
3:List 




3: Complex... 
ML i st... 
ST Matrix... 




bytes, etc.). 




6-W-Uars... 












RRM FREE 23489 










RRC FREE 131072 










► Li 66 










Lz 66 










Ls 12 










Lh 12 










Le 12 










Ls 12 










3. Move the cursor so that it points to 


B toL4 










RRM FREE 23489 




L4. 






RRC FREE 131072 








Li 66 










Lz 66 










Ls 12 










► Lh 12 










Le 12 










Ls 12 










4. Delete L4. 


TI-83 Plus: 










RRM FREE 23571 






\m 




RRC FREE 131072 




Note: Notice that no confirmation message 




Li 66 




displayed when you deleted this item. Confirmation 






Ls 66 
Ls 12 




messages only display when you delete an item 


TI-73: 




Le 12 




from Flash ROM (an application) or when you 


IENTERI 




► Ls 12 














(*) next to it, it is archived (TI-83 Plus only). 






5. I_4 no longer displays in the list editor. 
Use the arrow key ([►]) to scroll 


TI-83 Plus: 
ISTATl 1:Edlt|T1 










LS 


LE 


Lb E 








^M 


through the lists. 














Tip: See i Tip 6: Using Lists for information on 


TI-73: 

ilisti m 












how to use the SetUpEditor to put L4 back into the 




Lfi(1J= 




list editor. 







Topics in Algebra 1 



©2001 Texas Instruments 



1 Tip 10-3 



General Information 



Hardware and Software Requirements 



Hardware and Software Requirements 




Hardware and software 



Notes 



TI-73 with version 1 .60 or higher of the Graph 

Explorer software 

— or — 

TI-83 Plus or TI-83 Plus Silver Edition with version 

1 .14 or higher of the operating system software 



You can download a free copy of the latest Graph 
Explorer or operating system software from 
education.ti.com/softwareupdates. Follow the link 
to Operating Systems. 



Computer with Microsoft ® Windows® 95/98/2000, 
Windows NT®, or Apple® Mac® OS 7.1 or higher 
installed 



TI-GRAPH LINK™ computer-to-device cable 



If you do not have this cable, call your distributor, 
or order the cable from Tl's online store. 



TI-GRAPH LINK software that is compatible with the 

TI-73 or the TI-83 Plus 

— or — 

Tl™ Connect software, which works with all 

supported models of Flash-based Tl graphing 

devices. 



You can download free copies of TI-GRAPH LINK 
and Tl Connect software from 
education.ti.com/softwareupdates. Follow the link 
to Connectivity Software. 



Topics in Algebra 1 



© 2002 Texas Instruments 



1-1 



General Information 



Deleting an Application 



Deleting an Application 

TI-73 

1. Press [2nd] [MEM] to display the MEMORY menu. 

2. Select Delete. 

3. Select Apps. 

4. Move the cursor to the application name. 

5. Press I ENTER I . A confirmation message is displayed. 

6. Select Yes to delete the application. 




TI-83 Plus 

1. Press [2nd] [MEM] to display the MEMORY menu. 

2. Select Mem Mgmt/Del. 

3. Select Apps. 

4. Move the cursor to the application name. 



5. Press |DEL| . A confirmation message is displayed. 

6. Select Yes to delete the application. 



Topics in Algebra 1 



© 2002 Texas Instruments 



1-2 



General Information Installation Error Messages 




Installation Error Messages 
Low Battery 

Do not attempt to download a Flash application if the low-battery message appears on the home 
screen. Low battery indication is shown on the initial screen. If you receive this error during an 
installation, change the batteries before trying again. 

Invalid Signature or Certificate 

Either this device does not have a certificate to run the application, or electrical interference 
caused a link to fail. Try to install the application again. 

Error in Xmit 

This problem is usually associated with the unit-to-unit cable and its connection between the 
devices. Make sure the cable is firmly inserted in the link port of each device. 

Communication Error 

This error indicates that the TI Connect™ software ("Unable to communicate with device") or 
TI-GRAPH LINK™ software ("Link Transmission Error") is unable to communicate with the 
device. The problem is usually associated with the TI-GRAPH LINK cable and its connection to 
the device or to the computer. 

• Make sure the cable is firmly inserted in the device link port and the computer. 

• Verify that the correct cable type is selected in the software link settings. 

• Verify that the correct communications port (Com Port) is selected in the software link 
settings. (This does not apply if you use the USB port and TI Connect software.) 

Archive Full 

This error occurs when the TI-83 Plus does not have sufficient memory for the application. In 
order to make room for another application, you must delete an application or archived 
variables from the TI-83 Plus. Before you delete an application from the TI-83 Plus, you can save 
it on your computer using TI Connect or TI-GRAPH LINK™ software for the TI-83 Plus. You can 
reload it to the TI-83 Plus later using TI Connect or TI-GRAPH LINK software. 

Memory Error 

This error occurs when the TI-73 does not have sufficient memory for the application. In order 
to make room for another application, you must delete an application from the TI-73. Before 
you delete an application from the TI-73, you can save it on your computer using TI Connect 
software or TI-GRAPH LINK software for the TI-73. You can reload it to the TI-73 later using 
TI Connect or TI-GRAPH LINK software. 

Other Errors 

See Appendix B in the TI-73 guidebook or pages B-6 through B-10 in the TI-83 Plus guidebook 
for information about the specific error. 

Topics in Algebra 1 © 2002 Texas Instruments 1-3 



General Information Checking Version Numbers and Free Space 




Checking Version Numbers and Free Space 



Verify Operating System Version and ID Number 

The Topics in Algebra 1 application is compatible with TI-73 Graph Explorer software version 
1.60 and higher or the TI-83 Plus operating system 1.14 and higher. 

To verify your operating system version number: 

1. From the home screen, press |2nd| [MEM]. 

2. Select ABOUT. 

The operating system version number is displayed below the product name and has the format 
x.yy. The ID number appears on the line below the product number. 

Verify Flash Application Version 

The version number appears on the information screen below the application name. To display 
the information screen, do one of the following: 



• Press IAPPSI , and then select MathHand. 
— or — 

• Select INFO from the application's SELECT AN OPERATION menu. 

Check Amount of Flash Application Free Space 

TI-73 

1. From the home screen, press |2nd| [MEM]. 

2. Select Check Apps. 

The Math by Hand application requires one free space to load the application. 

For more information about memory and memory management, refer to the TI-73 guidebook. 

TI-83 Plus 

1. From the home screen, press |2nd| [MEM]. 

2. Select Mem Mgmt/Del. 

The Math by Hand application requires at least 16,384 bytes of ARC FREE (Flash), or one space, 
to load the application. 

For more information about memory and memory management, refer to the TI-83 Plus 
guidebook. 

Topics in Algebra 1 © 2002 Texas Instruments 1-4 



General Information Support and Service Information 




Texas Instruments (Tl) Support and Service Information 
For General Information 

E-mail: ti-cares@ti.com 

Phone: 1-800-TI-CARES (1-800-842-2737) 

For US, Canada, Mexico, Puerto Rico, and Virgin Islands only 

Home page: http://education.ti.com/ 

For Technical Questions 

Phone: 1-972-917-8324 

For Product (Hardware) Service 

Customers in the US, Canada, Mexico, Puerto Rico, and Virgin Islands: Always contact 
TI Customer Support before returning a product for service. 

All other customers: Refer to the leaflet enclosed with your product (hardware) or contact 
your local TI retailer/distributor. 



Topics in Algebra 1 © 2002 Texas Instruments 1-5 



End-User License Agreement 
Calculator Applications 



IMPORTANT - Read this agreement ("Agreement") carefully before Installing the software program(s) and/or calculator application(s). The 
software program(s) and/or calculator program(s) and any related documentation (collectively referred to as the Program) are licensed, not 
sold, by Texas Instruments Incorporated (Tl) and/or any applicable licensors (collectively referred to as Licensor). By installing or otherwise 
using the Program, you agree to be bound by the terms of this license. If the Program was delivered to you on diskette(s) or CD and you do 
not agree with the terms of this license, return this package with all its contents to the place of purchase for a full refund of any license fee 
paid. If the Program was delivered to you over the Internet and you do not agree with the terms of this license, do not install or use the 
Program and contact Tl for instructions on obtaining a refund of any license fee paid. 

Specific details of the license granted depend upon the license fee you paid and are set forth below. For purposes of this Agreement, a site ("Site") 
consists of one entire physical campus of an educational institution accredited by an association recognized by the U.S. Department of Education or the 
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SINGLE USER LICENSE 

If you paid a license fee for a Single User License, Licensor grants to you a personal, non-exclusive, non-transferable license to install and use the 
Program on a single computer and calculator. You may make one copy of the Program for backup and archival purposes. You agree to reproduce all 
copyright and proprietary notices shown in the Program and on the media. Unless otherwise expressly stated in the documentation, you may not 
duplicate such documentation. 

EDUCATIONAL MULTIPLE USER LICENSE 

If you paid a license fee for an Educational Multiple User License, Licensor grants you a non-exclusive, non-transferable license to install and use the 
Program on the number of computers and calculators specified for the license fee you paid. You may make one copy of the Program for backup and 
archival purposes. You agree to reproduce all copyright and proprietary notices shown in the Program and on the media. Except as expressly stated 
herein or in the documentation, you may not duplicate such documentation. In cases where Tl supplies the related documentation electronically, you 
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computers and calculators on which the Program is used must be located at a single Site. Each member of the institution faculty may also use a copy of 
the Program on an additional computer/calculator for the sole purpose of preparing course materials. 

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If you paid a license fee for an Educational Site License, Licensor grants you a non-exclusive, non-transferable license to install and use the Program on 
all institution, teacher, or student owned, leased or rented computers and calculators located or used at the Site for which the Program is licensed. 
Teachers and students have the additional right to use the Program while away from the Site. You may make one copy of the Program for backup and 
archival purposes. You agree to reproduce all copyright and proprietary notices shown in the Program and on the media. Except as expressly stated 
herein or in the documentation, you may not duplicate such documentation. In cases where Tl supplies the related documentation electronically, you 
may print one copy of such documentation for each computer or calculator on which the Program is installed. Each member of the institution faculty 
may also use a copy of the Program on an additional computer/calculator for the sole purpose of preparing course materials. Students must be 
instructed to remove the Program from student-owned computers and calculators upon the end of their enrollment in the institution. 

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Although no warranty is given for the Program, the media, if the Program was delivered to you on diskette(s) or CD, will be replaced if found to be 
defective during the first ninety (90) days of use, when the package is returned postage prepaid to Tl. THIS PARAGRAPH EXPRESSES LICENSOR'S 
MAXIMUM LIABILITY AND YOUR SOLE AND EXCLUSIVE REMEDY FOR DEFECTIVE MEDIA. 

LICENSOR SHALL NOT BE RESPONSIBLE FOR ANY DAMAGES CAUSED BY THE USE OF THE PROGRAM, OR SUFFERED OR INCURRED 
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EVEN IF LICENSOR HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. IN JURISDICTIONS WHICH ALLOW TEXAS 
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Because some states or jurisdictions do not allow the exclusion or limitation of incidental or consequential damages or limitation on how long an implied 
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GENERAL 

This Agreement will immediately terminate if you fail to comply with its terms. Upon termination of this Agreement, you agree to return or destroy the 
original package and all whole or partial copies of the Program in your possession and so certify in writing to Tl. 

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If the Program is provided to the U.S. Government pursuant to a solicitation issued on or after December 1 , 1995, the Program is provided with the 
commercial license rights and restrictions described elsewhere herein. If the Program is provided to the U.S. Government pursuant to a solicitation 
issued prior to December 1 , 1 995, the Program is provided with "Restricted Rights" as provided for in FAR, 48 CFR 52.227-1 4 (JUNE 1 987) or DFAR, 
48 CFR 252.227-701 3 (OCT 1 988), as applicable. 

Manufacturer is Texas Instruments Incorporated, 7800 Banner Drive, M/S 3962, Dallas, Texas 75251 . 

04/13/00 [ltem#] 

l:\Legal lnformation\Support&Serv, Warranty, & Licenses\Licenses\Calcapps\Standard\Sold_doc\sold-cal-app-eng.doc